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BRAINIAC S^~ 



The 1958 Experiments 



Edmund C. Berkeley 



Copyright 1958 by Berkeley Enterprises, Inc. 



Published by Berkeley Enterprises Inc. 

815 Washington St. 

Newtonville 60, Mass. 



First Printing, Sept. 1958 



Introduction 

Our Brainiacs, Geniacs, and Tyniacs - small electric 
brain machines - have now been evolving since 1950. That year 
we completed Simon, a complete miniature automatic digital com- 
puter using 129 relays, and started on "Simon Half", a simple 
construction kit for an electric brain. 

The first 33 Brainiacs were called Geniacs No. 1 to No. 
33, and were published in 1955; they are the same as Brainiacs 
No. 1 to No. 33. The next 13 Brainiacs (1956) were called 
Tyniacs No. 1 to No. 13; they are the same as Brainiacs No. 34 
to No. 46. The third installment (1957) of 60 small machines 
or experiments were called "Brainiacs - the New Experiments" 
and were numbered SI to S9, Ql to Q16, CI to C24, LI to L5, 
and Ml to M6; they are the same as Brainiacs No. 47 to No. 106 
respectively. The 45 additional machines (1958) are Brainiacs 
No. 107 to No. 151. 

Many of these 1958 Brainiacs have the same circuit dia- 
grams as previous machines, because of the limited variety of 
simple circuits; so they can be constructed by simply chang- 
ing appropriately the labels (of switches, positions, and 
lamps) for a previous machine. About 25 of the 1958 Brainiacs 
require new circuit diagrams which are here given. 

Brainiacs No. 132 to 144 constitute a considerable intro- 
duction to the algebra of logic, also called Boolean algebra, 
named after George Boole, a great English mathematician who 
lived 1815 to 1864. This algebra is a technique for manipu- 
lating AND, OR, NOT, and conditions, statements, or classes. 
This algebra is becoming rather important in the design of 
circuits for computing and controlling. In this connection, 
please see also Brainiacs LI and L2 in the 1957 collection. 

Brainiacs No. 125 to 128 relate to what is called the 
mathematical theory of groups, but simply give some interest- 
ing examples, to stir curiosity. 

We hope that you will be amused and entertained, and will 
find your curiosity whetted by these Brainiacs. We shall be 
glad to hear from you if you have comments, suggestions, 
corrections, or new experiments. 



Newtonville, Mass 

August, 1958 Edmund C. Berkeley 



2 - 



CONTENTS 

EXPERIMENTS 

Section 1. Safety and Alarm Circuits 



Page 



107. Atomic Reactor 5 

108. Puffin Bay Signaling System 5 

109. Burglar Alarm With Three Stations 5 

110. Maria Benedetto's Permission to Get Married 7 

111. Street Lighting in Duntown 7 

112. Paradise or Violent Death 7 

Section 2. Quiz and Puzzle Machines 

113. Five Words That Sound Alike 8 

114. Word Puzzle With C 8 

115. Planets of the Solar System 8 

116. A Geology Quiz 10 

117. Color Mixing 10 

118. Volcano Quiz 10 

119. Guessing a Lady's Age 11 

120. The Identification of Gold 12 

121. Latin and Greek Number Prefixes 12 

122. Good Bets in Spelling 13 

Section 3. Computing Machines 

123. Employment in a Cotton Mill 14 

124. Employment on a Railroad 14 

125. Turn Over, and Turn Around 14 

126. 2 f -1, and 1/2 16 

127. One, Zero, and Infinity 16 

128. One Divided By . . . and One Minus ... 16 

129. Another Translator from Decimal to Binary 18 

130. Another Translator from Binary to Decimal 18 

131. Translator from Decimal to Excess Three 21 

Section 4. Logical Machines 

132. The Main Concepts of Boolean Algebra 21 

133. Translation into Standard Expressions of Boolean 22 

Algebra 

134. Translation into Standard Statements of Boolean 24 

Algebra 

135. Summary of Rules for Calculating with Boolean 24 

Algebra — I 



Page 



136. Summary of Rules for Calculating With Boolean 25 

Algebra — II 

137. The Financial, General, and Library Committees 25 

138. Logical Sum 26 

139. Least Common Multiple 28 

140. Logical Product 28 

141. Highest Common Factor 28 

142. Logical Negation 29 

143. Complementary Factor 29 

144. Logical Exception 31 

145. Matching 31 

146. Merging 31 

147. Selecting 33 

148. The Merrimac and Eastern Timetable 33 

Section 5. Miscellaneous Machines 
(including Signaling and Game-Playing) 

149. The Theater Sign "Hamlet" 35 

150. The News Sign of the Kaltroit Dispatch 35 

151. A Variation of Nim 35 



4 - 



EXPERIMENTS 



107. ATOMIC REACTOR 

Problem : An atomic reactor is controlled by the degree to 
which control rods are in or out of the reactor. It has a 
warning lamp DANGER. Connected to the rods is an electric 
sensing button which will light the lamp when the rods are 
positioned in an unsafe position. 

Design a machine which will express the condition. 

Solution : The machine will have one switch POSITION OF RODS, 
which has two switch positions OK, UNSAFE. There will be one 
lamp marked DANGER. 

The circuit diagram is the same as Tyniac No. 1, with the 

labels appropriately changed. 



108. PDFFIN BAY SIGNALING SYSTEM 

Problem : In Puffin Bay there is a lighthouse on a rock about 
a mile from shore, and a coast guard station on the adjacent 
mainland. Between them is a cable. At each end, there is a 
key switch, and a signal light. The lighthouse can signal the 
land station, flashing its signal light; and the land station 
can signal the lighthouse, flashing its signal light. 

Design a machine which will fulfill these requirements. 

Solution : There will be two operating sets, each consisting 
of one switch and one lamp; one set will be labeled LIGHTHOUSE, 
the other set will be labeled LAND STATION. Between them will 
be a cable of four wires. Each of the switches will have two 
positions OFF and ON. The circuit is shown in Diagram 108. 



109. BURGLAR ALARM WITH THREE STATIONS 

Problem : Hubert Cromwell is positive that if a burglar enters 
his house, it will be either through the front cellar window, 
or through jimmying the front door, or through cutting the wire 
screening and unhooking the kitchen screen door. He sets elec- 
trical devices which will detect whether any of these three 
things happen. He desires two lamps GREEN — ALL IS WELL, and 
RED — BURGLAR, to shine on the front of his house where the 
police can see them. Design the circuit required. 



108. PUFFIN BAY SIGNALING SYSTEM 




Signal Light 



Signal Light *=±=- 



113. FIVE WORDS THAT SOUND ALIKE 
J 
P. 




jklmnopqr t 

(Ml (£>(?) (ft (?)(?) (?)&(?) 

A S Z E 1 



C S E E I 



6 - 



Solution : There will be three switches FRONT CELLAR WINDOW , 
FRONT DOOR and KITCHEN SCREEN DOOR, each with two positions 
SHUT and FORCED OPEN. The two lamps have been mentioned. The 
circuit is the same as Brainiac S5 with the labels changed ap- 
propriately. 



110. MARIA BENEDETTO'S PERMISSION TO GET MARRIED 

Problem : Maria Benedetto can get married only if her mother, 
Doria, her two Italian grandmothers, Felicia and Fidelia, and 
her mother's two sisters, Angelina and Alicia, all see theywng 
man, and give their explicit OK. 

Design a machine which will show when she can get married. 

Solution : There will be five switches DORIA, FELICIA, FIDELIA, 
ANGELINA, and ALICIA. Each switch will have two positions NO 
and OK. There will be one lamp, MARIA'S MARRIAGE APPROVED. The 
circuit is the same as Brainiac S3, with the labels changed ap- 
propriately. 



111. STREET LIGHTING IN DUNTOWN 

Problem : The city of Dun town desires to have its street lamps 
lighted between a half hour after sunset and a half hour before 
sunrise, except that when it is darker than a certain standard, 
the lights should also go on. 

Design the circuit. 

S olution : There will be two switches. One switch will be TIME 
OF DAY, with two positions, one BETWEEN HALF HOUR AFTER SUNSET 
AND HALF HOUR BEFORE SUNRISE, and the other position OTHER TIMES. 
The second switch will be BRIGHTNESS, with two positions, DARKER 
THAN A CERTAIN STANDARD, and NOT SO DARK. There will be one 
lamp labeled STREET LIGHTS LIGHTED. The circuit will be the 
same as Brainiac S4, with appropriate changes in the labels. 



112. PARADISE OR VIOLENT DEATH 

Problem : The King of Sandillia has installed a garden of para- 
dise in a secluded valley in his kingdom. He requires each of 
his prime ministers, after three years in office, to choose one 
of five corridors in his palace. Four of the corridors lead to 
precipitous drops into space off mountain-sides, the fifth to 
the garden of paradise. 

- 7 - 



Set up these conditions in a machine. 

Solution : There will be one switch labeled CHOICE OF CORRIDOR 
with five positions l f 2, 3, 4, 5. There will be two lamps, one 
marked VIOLENT DEATH, the other PARADISE. Connect one of the 
switch points to the PARADISE lamp, the other four to the VIOLENT 
DEATH lamp. Let no one know how you have wired your machine. 
After your friend as prime minister has chosen his corridor, 
turn the on-off switch to "on", to show the effect of his choice. 

113. FIVE WORDS THAT SOUND ALIKE 

Problem : There are five words that sound almost exactly alike. 
Their meanings are: (1) oceans; (2) take; (3) regards; (4) 
plural of a letter of the alphabet; (5) stop. 

Set up a machine that will shine these words in lights. 

Solution : There will be one switch MEANING OF WORD with five 
positions 1, 2, 3, 4, 5. There will be ten lamps C, S, E, E, 
I, ' , A, S, Z, E. The circuit appears in the diagram. 

114. WORD PUZZLE WITH C 

Proble m: Using the nine letters C, D, E, I, P, R, S, T, U, 
words with the following meanings can be made: 



1. 


a point 


5. 


tooth 


2. 


small open containers 


6. 


hints 


3. 


severs 


7, 


dogs 


4. 


a god of love 


8. 


short 



Design a machine which will show these words. 

Solution : There will be one switch MEANING OF WORD with eight 
positions 1 to 8. There will be two labels C, U, at the left, 
and seven lamps to the right of them with labels S, R, P, T, 
ID, E, S. The circuit appears in the diagram. (The answers are: 
CUSP, CUPS, CUTS, CUPID, CUSPID, CUES, CURS, CURT, respective- 
ly.) 



115. PLANETS OF THE SOLAR SYSTEM 

Problem : Make a machine which will answer the following ques- 
tions: 

1. Which planet is farthest from the sun? 

- 8 - 



114. WORD PUZZLE WITH C 
Si 

1/ 




( £)(£>(?)(£>(£)(£)(?) 

CUSRPTIDES 



117. COLOR MIXING 



Br O 




Red 



Yellow 



P Blue ^Y 



R O Y G Bl 



( ?) (£> (3) (S) (fr (?) (ft 

Red Orange Yellow Green Blue Purple Brown 



- 9 



2. Which planet is nearest to the earth? 

3. Which planet has no atmosphere? 

4. Which planet is the biggest? 

5. Which planet has a ring around it? 

6. Which planet is the most likely to be first 

visited by men? 

Solution : There will be one switch labeled QUESTION, with six 
positions 1 to 6. There will be six lamps labeled PLUTO, VENUS, 
MERCURY, JUPITER, SATURN, MARS. (These are the answers to the 
six questions, respectively.) The circuit diagram is the same 
as Brainiac Q10, except that positions and lamps 7, 8, 9, 10 
are not used. 



116. A GEOLOGY QUIZ 

Proble m: Make a machine which will answer the following ques- 
tions: 

1. In what era was the most coal deposited? 

2. What was the earliest horse? 

3. What was the largest dinosaur? 

4. What was the earliest common crustacean? 

5. What was the earliest known bird? 

6. What great prehistoric animal is occasionally 

found frozen and undecayed in the Arctic? 

Solutio n: The solution is the same as the preceding solution, 
with labels changed appropriately. (The answers to the ques- 
tions are, CARBONIFEROUS, EOHIPPUS, GIGANTOSAURUS , TRILOBITE, 
ARCHEOPTERYX , WOOLLY MAMMOTH) . 



117. COLOR MIXING 

Problem: What are the colors which you obtain by mixing any 
one or more of red, yellow, and blue, the three primary colors? 
Design a machine which will show them. 

Solution: There will be three switches RED, YELLOW, BLUE, each 
with two positions ABSENT, PRESENT. There will be seven lamps 
RED. ORANGE, YELLOW, GREEN, BLUE. PURPLE and BROWN. The circuit 
appears in the diagram. 



118. VOLCANO QUIZ 

Proble m: Design a machine which will answer the following ques- 
tions: 

- 10 - 



1. What volcanic explosion caused an island to 

disappear, and was heard for 2500 miles? 

2. What volcano caused 30,000 deaths in the West 

Indies? 

3. What was the greatest volcanic explosion in 

historic times? 

4. What volcano destroyed Pompeii? 

5. What is the most famous volcano in Europe? 
6* What is the highest volcano in Africa? 

7. What is the only volcano in the United States? 

Solution : There will be one switch labeled QUESTION with seven 
positions 1 to 7. There will be seven lamps labeled KRAKATOA, 
1883; MONT PELEE, 1902; TAMBORA, 1815; MONTE SOMMA. 79 A.D.; 
VESUVIUS; KILIMANJARO; LASSEN. (These are the answers to the 
seven questions, respectively) . The circuit diagram is the 
same as Brainiac Q10, except that positions and lamps 8, 9, 10 
are not used. 



119. GUESSING A LADY'S AGE 

Problem : You have a friend who won't tell how old she is. How- 
ever, you believe she can be persuaded to answer four questions 
verbally "yes" or "no" about her age; and you also believe that 
you can judge what ten-year interval of age (decade) she is in. 

Design a machine which will tell how old she is 

Solution : Here is one of many designs. Switch A asks the 
question: "Does the last digit of your age end in 2, 3, 6, 7, 
8, or 9?" Switch B asks the question: "Is your age an odd num- 
ber?" Switch C asks the question: "Does your age end in 0, 1, 
2, or 3?" Switch D asks the question: "Does your age end in 6 
or 7?" Each switch will have two positions, YES and NO. 

There will be ten lamps numbered with the digits to 9 
(the last digit of the lady's age, if she has answered the 
questions truthfully) . 

After your friend has answered these questions, take a 
good look at her, and estimate what decade she is probably in; 
for example if the lamp that lights is a 5, you should be able 
to tell by looking at her whether her age is 35, or 45, or 55, 
etc. 

The circuit is the same as the circuit for Brainiac Q5, 
with appropriate changes of labels. 



11 - 



120. THE IDENTIFICATION OF GOLD 

Problem : John O'Leary, prospector, finds a rock with golden 
yellow particles in it. Is this gold, or altered mica, or py- 
rite (fool's gold, iron sulphide) or chalcopyrite (copper iron 
sulphide)? 

Design a machine which will identify the specks for him as 
gold if they are gold. 

Solution : There will be three switches, one for each of the 
following questions; each switch will have two positions, YES, 
NO. 

1. SOFT: Are the golden particles in the rock easily 

scratched and grooved with a knife? (If yes, 
may be altered mica, chalcopyrite, or gold; if 
rfot, pyrite.) 

2. HEAVY: If the particles are mixed with iron fillings 

in a little glass bottle, do they sink to the 
bottom? (If yes, probably gold; if not, prob- 
ably pyrite or chalcopyrite; if float on top, 
mica. ) 

3. MALLEABLE: If a particle is gently hammered with a 

hammer, does it spread out, is it malleable? 
(If yes, it is gold; if it crushes into a pow- 
der, it is not gold.) 
There will be one lamp IT IS GOLD. The circuit is the same as 
Brainiac S2, with appropriate changes of labels. 



121. LATIN AND GREEK NUMBER PREFIXES 

Problem : Many English words have prefixes that come from the 
Latin or the Greek. Some common prefixes express number. 

Design a machine which will take in the numbers "half, 
one, two, five, ten, hundred, thousand, many, first" and indi- 
cate the Latin or Greek prefix that has that meaning. 

Solution : There will be one switch NUMBER with nine positions, 
one for each number given above. There will be nine lamps. On 
the first row under each lamp will be the prefix from the Latin; 
on the. second row under each lamp will be the prefix from the 
Greek. 

English Latin Greek 

(Switch Position) (Lamp) (Lamp) 

half semi hemi 

one uni mono 

two bi di 

- 12 - 



five 


quint 


ten 


deci 


hundred 


centi 


thousand 


milli 


many 


multi 


first 


prim 



penta 

deca 

hecto 

kilo 

poly 

proto 

The circuit is the same as the diagram for Brainiac C18, 

with appropriate changes of labels. 



122. GOOD BETS IN SPELLING 

Problem : All English words contain a selection of 43 sounds. 
There are however only 26 letters to spell them with. Some 
sounds though can be spelled in one and only one way. These 
include the sounds b t d, h, 1, m t n; if you hear one of these 
sounds, it is a sure bet that it is spelled using that letter. 
Some of the other sounds in English words are very good bets. 
For example, the sound M f" as in "if", is spelled in only 
three ways; the sound "ng" as in "sing" is spelled in only two 
ways; the sound "oi" as in "poison" is spelled in only two 
ways. 

Design a machine which will show the good bets for spell- 
ing the sounds f, ng, and oi. 

Solution : The machine will have one switch labeled ENGLISH 
SOUND with seven positions: f, 1st spelling; f, 2nd spelling; 
f, 3rd spelling; ng, 1st spelling; ng, 2nd spelling; oi, 1st 
spelling; oi, 2nd spelling. There will be seven lamps. The 
lamps will have labels as follows: 

1. Spelled "f", in many short words, and all words from 
Latin; as in "fox, muff, confident" 

2. Spelled "ph" in many words nearly all from Greek; 
"nymph, graph, telephone" 

3. Spelled "gh"; rare; about eight words from Anglo 
Saxon, and only as the final sound; "cough, rough, 
tough, laugh, enough, trough, draught, slough" 

4. Spelled "ng" almost always; "sing, finger, singer, 
anger" 

5. Spelled "n", in a few words before the sound "k"; 
"ink, conquer" 

6. Spelled "oi" often, usually initial or medial; "oil, 
poison, avoid" 

7. Spelled "oy", usually final, rarely not final; "boy, 
toy, oyster" 

The circuit is the same as for Brainiac C18 or C19, with 
appropriate changes of labels. 



- 13 - 



123. EMPLOYMENT IN A COTTON MILL 

Problem : The number of persons employed in the Rogers Cotton 
Mill in Wollaston is reported as follows: 
Married Unmarried 

Male 301 493 

Female 582 674 

Design a machine which will tell the total number of 
males, females, married, unmarried and total employees. 

Solution : There will be three switches, one with positions 
MALE, FEMALE, TOTAL, and the other with positions, MARRIED, 
UNMARRIED, TOTAL. There will be five lamps: TOTAL MALE, 
TOTAL FEMALE, TOTAL MARRIED, TOTAL UNMARRIED, TOTAL EMPLOYEES. 
The circuit is shown in the diagram. 



124. EMPLOYMENT ON A RAILROAD 

Problem : The number of persons employed on the Oklahoma and 
Alaska Railroad is reported as follows: 

White Non-White 

Married Unmarried Married Unmarried 
Males 328 225 425 317 
Females 193 137 154 132 

Design a machine which will tell the total number of 
males, females, married, unmarried, white, and non-white, and 
total employees. 

Solution : There will be three switches: one, with positions 
MALE, FEMALE, TOTAL; the second, with positions MARRIED, UN- 
MARRIED, TOTAL; and the third, with positions WHITE, NON- 
WHITE, TOTAL. There will be seven lamps: TOTAL MALE, TOTAL 
FEMALE, TOTAL MARRIED, TOTAL UNMARRIED, TOTAL WHITE, TOTAL 
NON-WHITE, TOTAL EMPLOYEES. The circuit is shown in the 
diagram. 



125. TURN OVER, AND TURN AROUND 

Problem : Tom Adler, math student, notices that if he takes a 
rectangle, he can turn it over, or turn it around, or both, 
and that he will still have a rectangle of the same shape and 
in the same position as he had to begin with. He marks the 
original rectangle with the letter R, and notices what happens 
in each of the four positions with each operation. 



- 14 



123. EMPLOYMENT IN A COTTON MILL 




Sex 



Marriage Status 
L4 



LI L2 L3 L4 L5 

(?)(?) 0) 0) 0) 



Total Total Total 

Male Female Married 

794 1256 883 



Total Total 1 

Unmarried Employees 
1167 2050 



124. EMPLOYMENT ON A RAILROAD 




Sex 



White 



Marriage Status 



Color 



LI 



L2 



L3 



L4 



L5 



L6 



L7 



( ft (ft @ (ft (ft (ft 0) 



Total Total Total Total Total 

Male Female Married Un- White 

Married 



1295 



616 



1100 



811 
15 - 



883 



Total Total ? 
Non- Em- 
White ployees 

1028 1911 



Design a machine which will show what happens to the R 
for each operation. 

Solution : There will be one switch POSITION OF R which will , 
have four positions, R . 9i ,B\ a, and a second switch OPERATION 
which will have three positions TURN OVER, TURN AROUND, and 
BOTH. There will be four lamps labeled R, 51 , tf , J) showing 
the results. The circuit is shown in the diagram. 



126. 2 AND -1 AND J£ 

Problem : Tom Adler notices that if he takes the number 2, and 
applies to it the operations ONE MINUS ..., and ONE DIVIDED 
BY ..., and their repetitions, he obtains only 2, -1, }£, be- 
cause: 

1 - (2)= -1, 1 - (-1) = 2, 1 - G£) =* y 2 
1 * (2)a J£ t 1 t G£) - 2, 1 -f- (-1) =* -1 

Design a machine which can be set at any of the numbers 
2, -1, J£, and at either of the operations ONE MINUS ..., and 
ONE DIVIDED BY . . . and which will show the correct result. 

Solution : There will be two switches, one NUMBER, with the 
positions 2, -1, J£, and the other OPERATION, with the two 

positions ONE MINUS ..., and ONE DIVIDED BY There will 

be three lamps 2, }£, -1. The circuit is shown in the diagram. 



127. ONE, ZERO, AND INFINITY 
Problem : Wondering if there are any other numbers like this, 



Tom Adler notices that: 






1 - 1 m 1 


-0 = 1 


1 - 00 =00 


1 r 1 = 1 1 


■j = oo 


1 -f oo = 



Design a machine which will show these results. 

Solution : The same machine as for the preceding problem will 
apply, except that the labels change and the wiring between 
the OPERATION switch and the lights is slightly different. 
The changes can be readily reasoned out. - 



128. ONE DIVIDED BY . . . , AND ONE MINUS . . . 

Problem : Tom Adler notices that if he takes the number 4 and 
applies the operations ONE DIVIDED BY . . . and ONE MINUS ... 
to 4, and to any of the numbers yielded by repeated applica- 

- 16 - 



125. TURN OVER, AND TURN AROUND 




urn Around 
ezzaJt Turn Over 



Position of R 4 Operation 

12 3 4 

Result 



R 



H 



ZL 



126. 2 AND -1 AND 1/2 




One Divided 
By.... 

'^\ One Minus . 



Number 



Operation 



-1 



1/2 -dt 



- 17 



tions of these operations, the only numbers that he gets are 
4, -3, 1/4, -1/3, 4/3, and 3/4. He notices that if jn is any 
number, then the only different operations that he gets are 
1-n, 1/n, l/(l-n), n/(n-l), and (n-D/n. He wants a machine 
which he can set at any number 4, -3, 1/4, -1/3, 4/3, 3/4 and 
any of the five operations, and which will show the result of 
the selected operation on the selected number. 

Solution : There will be two switches, one NUMBER with the six 
positions 4, -3, 1/4, -1/3, 4/3, 3/4 and the other OPERATION 
with the five positions 1-n, 1/n, V(l-n), n/(n-]), (n-Dn. There will 
be six lamps 4, -3, 1/4, -1/3, 4/3, 3/4. The circuit is 
shown in the diagram. 



129. ANOTHER TRANSLATOR FROM DECIMAL TO BINARY 

Problem : Numbers may be expressed not only in decimal nota- 
tion, the scale of ten using the digits to 9, but also in 
binary notation, notation in the scale of two using only the 
digits and 1. Following is the translation of the first 
ten numbers in decimal notation into their equivalents in 
binary notation: 



Decimal 


Binary 


Decimal 


Binary 








5 


101 


1 


1 


6 


110 


2 


10 


7 


111 


3 


11 


8 


1000 


4 


100 


9 


1001 



In binary notation the positions of the digits count, from 
right to left, units, twos, fours, eights, sixteens, etc. 
Thus the binary number 1101 is 1 eight, plus 1 four, plus 
twos, plus 1 one, or thirteen. 

Design a machine which will accept any number from to 
9 in decimal notation and shine in four lights its translation 
into binary notation. 

Solution : The solution is shown in the circuit diagram. 



130. ANOTHER TRANSLATOR FROM BINARY TO DECIMAL 

Problem : Given any one of the binary numbers from to 1001, 
design a machine which will shine in lights the decimal num- 
ber to 9. 

Solution : There will be four switches, one for each of the 
binary digits: BINARY EIGHTS DIGIT, BINARY FOURS DIGIT, BIN- 
ARY TWOS DIGIT, and BINARY ONES DIGIT. Each of these switches 

- 18 - 



128. ONE DIVIDED BY ... , AND ONE MINUS . . . 
4 ^Zi 3/4 




Number n 




4/3 -V« 

Operation 








4 -3 1/4 -1/3 4/3 3/4 ~1 

129. ANOTHER TRANSLATOR FROM DECIMAL TO BINARY 
5 V4 




Decimal Number Switch 
L2 LI 



- 19 - 



130. ANOTHER TRANSLATOR FROM BINARY TO DECIMAL 

*31 

1 




Binary Fours Digit Binary Twos Digit 

r2 

10 ^4bzb{4i " hs2a\-r — >0 



Binary Ones Digit Binary Eights Digit 

(£)(£)(£)(£)(£)(£)(£)£)(£)(£) 

123456789 

Decimal Number 




131. TRANSLATOR FROM DECIMAL INTO EXCESS THREE 

.LI L2 




Binary Excess 
Three Number 

On = 1 
Off = 



L4 



L3 



L2 



LI 



(£)'(&) (3) - (?) , 

4th Digit 3rd Digit 2nd Digit 1st Digit JL 

- 20 - 






0011 


5 


1 


0100 


6 


2 


0101 


7 


3 


0110 


8 


4 


0111 


9 



will have two positions, or 1. There will be ten lights 
labeled to 9. The circuit appears in the diagram. Note 
that this machine will not translate correctly binary numbers 
greater than 1001. 



131. TRANSLATOR FROM DECIMAL TO EXCESS THREE 

Problem : The codes for the decimal digits to 9 in what is 
called "binary excess three" code are as follows: 

1000 

1001 

1010 

1011 

1100 

Design a machine which will translate from decimal to 
binary excess three. 

Solution : There will be one switch DECIMAL NUMBER, with posi- 
tions to 9. There will be four lamps for the four digits 
of the binary excess three code, from left to right 4TH DIGIT, 
3RD DIGIT, 2ND DIGIT, 1ST DIGIT. If a lamp is lighted the 
digit is 1; if it is not lighted the digit is 0. The circuit 
appears in the diagram. 



132. THE MAIN CONCEPTS OF BOOLEAN ALGEBRA 

Problem : Professor Higgins is giving a course in the algebra 
of logic in Edinburgh University. One day he assigns his 
students to bring in the next day the answer to "What are the 
nine important concepts of Boolean algebra, the algebra of 
classes?" 

Design a machine which will answer this question. 

Solution : There will be one switch IMPORTANT CONCEPTS OF 
BOOLEAN ALGEBRA. It will have nine positions 1 to 9. There 
will be 9 lamps labeled as follows: 

1. CLASSES: letters a., b, c., and so forth, stand for 

classes of things (not numbers) 

2. EQUALITY: a - b, a EQUALS b; true if and only if the 

things contained in the class a, are the same things 
that are contained in class b 

3. INEQUALITY: a 4 b, a DOES NOT EQUAL b; true if and 

only if there is at least one thing contained 
either in the class a, or the class b which is not 
contained in the other one. 

- 21 - 



4. LOGICAL SUM: avb, read a OR b; meaning a OR b OR 

BOTH; denoting the class of things contained either 
in the class .a or in the class b or in both. 

5. LOGICAL PRODUCT: a-b, or ab f read a AND b; meaning 

'BOTH a AND b; denoting the class of things contained 
both in the class a. and in the class j>. 

6. THE NULL CLASS: 0; nothing; emptiness; the class 

which contains nothing 

7. THE UNIVERSE CLASS: 1; all; everything; the class 

which contains all the things being discussed 

8. LOGICAL NEGATIVE: a\ read a prime, or NOT-a; the 

class of things being discussed that are NOT con- 
tained in the class a 

9. LOGICAL INCLUSION: aebT read "a is in b", or "a lies 

in b"; true if and only if all the things contained 
in a are contained also in the class b 
The circuit is the same as the diagram for Brainiac C18, with 
appropriate changes of labels. It may be desirable to mount 
the lamp socket vertically, so that adequate labels may be 
placed next to the lamps. See diagram C19. 



133. TRANSLATION INTO STANDARD EXPRESSIONS OF BOOLEAN ALGEBRA 

Problem : In another lecture, Professor Higgins writes the 
following 16 expressions on the blackboard, and asks his stu- 
dents to translate them correctly into standard Boolean ex- 
pressions: 

A's or B's but not both 
A's that are B's 
A's without B's 
A's, B's 

either A's or B's 
A's or B's or both 
A's excluding B's 
A's and/or B's 

OR meaning the inclusive 
... and ..."; NOT; and 
parentheses (used in the mathematical sense) to mark grouping. 

Design a machine which will give the correct translation. 

Solution : There will be one switch EXPRESSION, with 16 posi- 
tions numbered 1 to 16 corresponding with the expressions 
above. There will be seven lamps as follows: 



- 22 - 



1. 


A's except B's 


9. 


2. 


A's, also B's 


10. 


3. 


A's or else B's 


11. 


4. 


not both A's and B's 


12. 


5. 


neither A's nor B's . 


13. 


6. 


what are both A's and 


14. 




B's 


15. 


7. 


A's or B's 


16. 


8. 


A's and B's 




Standard Boolean expressions 


use: 


"or", 


"and/or"; AND meaning 


"both 



133. TRANSLATION INTO STANDARD EXPRESSIONS OF 
BOOLEAN ALGEBRA 

Qj^-^2 2 4 s»21 




0.9 Expression 



(?) $) (#•(?)(?) (?) (?) , 

23 -L 



Standard 
Boolean 
Expressions 17 18 



19 



20 



21 



22 



134. TRANSLATION INTO STANDARD STATEMENTS OF 
BOOLEAN ALGEBRA 



Standard 
Boolean 
Statement 




Statement 



( £)(£)(£)(£>(&)($)($) 



17 


18 


19 


20 


21 


22 


All A's 


Some A f s 


A ! s 


All A f s 


All B's 


No A f s 


are B f s 


are 


equal 


are 


are A*s 


are 




non-B ! s 


B's 


non-B f s 




B's 



23 ? 

Am- 
biguous 



23 



17. A's OR B's; A v B 21. NOT-(A's AND B's); (A-B)' 

18. A's AND B's; A-B 22. NOT-A's AND NOT-B f s; A'-B' 

19. A's AND NOT-B's; A-B' 23. Ambiguous 

20. (A's AND NOT-B's) OR (B's AND NOT-A's); A-B' v b-A' 
The circuit is shown in the diagram. 



134. TRANSLATION INTO STANDARD STATEMENTS OF BOOLEAN ALGEBRA 

Problem : In Professor Higgins' course in the algebra of logic 
(Boolean algebra) in Edinburgh University, he lectures one day 
on translating statements of ordinary English into standard 
statements in Boolean algebra. Professor Higgins writes the 
following 16 expressions on the blackboard, and asks his stu- 
dents to translate them correctly into standard Boolean state- 
ments. 

1. A's are B's. 9. It is an A only if it is 

2. The A's are B's. a B. 

3. It is an A if and only 10. A's are included in B's. 

if it is a B. 11. The A's are the B's. 

4. A's are not B's. 12. Every A is a B. 

5. Not all A's are B's. 13. Not every A is a B. 

6. If it is an A, it is a B. 14. Any A is a B. 

7. It is an A if it is a B. 15. Not any A is a B. 

8. None of the A's are B's. 16. A's include B's. 

Design a machine which will give the correct translation. 

Solution : There will be one switch EXPRESSION, with positions 
numbered 1 to 16 corresponding to the expressions above. 
There will be seven lamps labeled as follows: 

17. All A's are B's; AcB. 20. All A*s are non-B's; AcB' 

18. Some A's are non-B's; 21. All B's are A's; BcA 

A-B'^0 22. No A's are B's; AB= 

19. A's equal B's; A = B. 23. Ambiguous 

The circuit is shown in the diagram. 



135. SUMMARY OF RULES FOR CALCULATING WITH BOOLEAN ALGEBRA — I 

Problem : One day in Professor Higgins' class in the algebra 
of logic, he gives his students the assignment of bringing in 
the next day a summary of the rules for calculating with 
Boolean algebra that do not involve logical negation. 

Design a machine that will solve this problem. 



24 - 



= a v (b v c 
ab v ac; 


■ ); (ab)c = 


a (be) 


a 

i; 

A! 


a - a 

a(a v b) = 
a v = a; 
5S: a v 1 


a 

a.O = 

* 1; 





Solution : There will be one switch RULE with seven positions 
1 to 7. There will be seven lamps labeled as follows: 

1. COMMUTATIVE LAW: a v b = b v a; ab - ba 

2. ASSOCIATIVE LAW: (a v b) v c 

3. DISTRIBUTIVE LAW: a(b v c) = 

a v 'be * (a v b) (a v c) 

4. LAW OF TAUTOLOGY: a v a = a; 

5. LAW OF ABSORPTION: a v ab = a; 

6. LAWS INVOLVING THE NULL CLASS: 

7. LAWS INVOLVING THE UNIVERSE CLASS: 

a*l = a 
The circuit is the same as the diagram for Brainiac C18 with 
appropriate changes of labels. 



136. SUMMARY OF RULES FOR CALCULATING WITH BOOLEAN ALGEBRA — II 

Problem : The next day Professor Higgins assigns to his students 
presenting a summary of the remaining rules for calculating 
with Boolean algebra. 

Design a machine that will solve this problem. 

Solution : There will be one switch RULE with ten positions. 
There will be 10 lamps labeled as follows: 

1. EVERYTHING IS a OR NOT-a: 1 = a v a 1 ; 

1 = (a v a')(b v b'Hc v c 1 ) 

2. NOTHING IS BOTH a AND NOT-a: = a- a 1 

3. NEITHER ... NOR: (a v b) f = a'-b'; 

(a v b v c )* = a'-b'-c'.... 

4. NOT BOTH ... : (ab) 1 = a* v b f 

5. DOUBLE NEGATIVE: (a 1 )' = a 

6. ab v ab 1 » a; (a v b)(a v b') = a 

7. 0' - I; I 1 = 

8. acb is equivalent to ab 1 = O f or ab ■ a, or b'cra* 

9. a ■ b is equivalent to ab 1 v a'b = 0, or acb and 

be a 
10. x v y - is equivalent to x = and y = 
The circuit is the same as the diagram for Brainiac C18 f with 
appropriate changes of labels. 



137. THE FINANCIAL, GENERAL, AND LIBRARY COMMITTEES 

Problem : Professor Higgins states the following problem (due 

to John Venn) in the algebra of classes: 

A certain club has the following rules: (1) The finan- 
cial committee (f) shall be chosen from among the general 
committee (g). (2) No one shall be a member of both the 

- 25 - 



general and library committee (b) unless he is also on the 
financial committee. (3) No member of the library com- 
mittee shall be on the financial committee. Simplify 
these rules. 
He tells his students to bring in the solution to the problem 
the next day, worked out in a sequence of steps. 

Design a machine that will present the solution to the 
problem. 

Solution : There will be one switch STEP NUMBER with ten posi- 
tions 1 to 10. There will be 10 lamps, with the following 
1 shf* Is* 

1. TRANSLATING THE GIVEN CONDITIONS: (a) All f are .g: 

f <=9; fg*= (b) All that are both £ and b are f: 
gberf; gbf = (c) There are no members both _b 
and f: bf = 0. 

2. fg* v gbf v bf - : To combine given conditions, 

put each into a form equal to the null class, and 
connect with OR. 

3. fg* v bfg v bf(g v g') = : Using the rule 

a ~ a(c v c 1 ) 

4. fg' v bfg v bfg v bfg 1 = : Using the rule 

a(c v c') = ac v ac 1 

5. (fg' v bfg') v (bfg v bfg) = : Regrouping 

6. fg* v bg(f v f ) - 0: Using a v ac - a and 

ab v ac -■ a(b v c) 

7. fg 1 v bg = 0: Using a v a* = 1 and a* 1 = a 

8. fg' = 0, bg = 0: If x v y ■ 0, then x = and y = 

9. fcg = 0, bg = 0: If ac* = 0, then ace 

10. ANSWER: The rules may be simplified as follows: (1) 
The financial committee shall be chosen from among 
the general committee. (2) No member of the general 
committee shall be on the library committee. 
The circuit diagram is the same as diagram C18, with appro- 
priate changes of labels. 



138. LOGICAL SUM 

Problem : The logical sum of a class F and a class G is equal 
to the class every member of which is in F or in G or in both. 
The logical sum is written F v G where the v stands for the 
operation "and/or", the "inclusive or". is the null class, 
the class with no members. 1 is the universe class, the class 
of all things being discussed. 

Design a machine which will give the logical sum of two 
classes where either one may be or a or b or 1. 

- - 26 - 



138. LOGICAL SUM 
La 




LO 



La 



Lb 



Lc 



LI 



c = avb 



1 



140. LOGICAL PRODUCT 




LO 



LA 



LB 



LC 



B C=A-B 



LI 



"1 



27 



Solution : There will be two switches, the FIRST CLASS and the 
SECOND CLASS. Each will have four positions f .a, b, 1. There 
will be five lamps corresponding to the possible logical sums: 
0, a, b, c=a vb, and 1. The circuit appears in the diagram. 



139. LEAST COMMON MULTIPLE 

Problem : The least common multiple of a first number F and a 
second number G is the smallest number which contains both 
numbers as factors. 

Design a machine which will give the least common multiple 
of two numbers, where F may be any one of 1, 3, 5, 30, and G 
may be any one of 1, 3, 5, 30. 

Solution : There will be two switches, the FIRST NUMBER and 
the SECOND NUMBER. Each will have four positions 1, 3, 5, 30. 
There will be five lamps corresponding to the possible least 
common multiples 1, 3, 5, 15, 30. 

The circuit is exactly the same as the circuit for Logi- 
cal Sum, with appropriate changes of labels, because this 
problem has just the same structure as that problem. 



140. LOGICAL PRODUCT 

Problem : The logical product of a first class F and a second 
class G is equal to the class every member of which is both 
in F and in G. The logical product of two classes is written 
F-G, where the "•" (centered dot) stands for the operator 
"AND" in the meaning "both ... and ...". 

Design a machine which will give the logical product of 
two classes where either one may be 0, A, B, 1. 

Solution : There will be two switches, the FIRST CLASS F and 
the SECOND CLASS G. Each will have four positions, 0, A, B, 1. 
There will be five lamps corresponding to the possible products 
0, A, B, C = A-B, 1. 

The circuit appears in the diagram. 



141. HIGHEST COMMON FACTOR 

Problem : The highest common factor of a first number F and a 
second number G is the largest number which will go into both 

- 28 - 



numbers as a factor. 

Design a machine which will give the highest common fac- 
tor of two numbers F and G f where F may be any one of 1, 6 t 
10, 30 and G may be any one of 1, 6, 10, 30. 

Solution : There will be two switches, the FIRST NUMBER and the 
SECOND NUMBER. Each will have four positions 1, 6, 10, 30. 
There will be five lamps corresponding to the highest common 
factors 1, 2, 6, 10, 30. 

The circuit is exactly the same as the circuit for Logi- 
cal Product with appropriate changes of labels, because this 
problem has just the same structure as that problem. 



142. LOGICAL NEGATION 

Problem : The logical negative of a class F is equal to the 
class every member of which is in the class of all things be- 
ing discussed but is not in the class F. The logical negative 
of the class F is written F' (read F prime) and is called 
NOT-F. 

Design a machine which will give the logical negative of 
a class F which may be any one of 0, A, B, A*B, A v B, 1. 

Solution : There will be one switch THE CLASS, with six posi- 
tions 0, A, B, A-B, A v B, 1. There will be six lamps corre- 
sponding to the possible negatives 0, A 1 , B 1 , A'-B 1 , A 1 v B 1 , 
1. 

The circuit appears in the diagram. 



143. COMPLEMENTARY FACTOR 

Problem : The complementary factor of a number is equal to the 
result of dividing this number into the largest number being 
considered. For example; if 210 is the largest number being 
considered, the complimentary factor for 30 is 7. 

Design a machine which will give the complementary factor 
of a number which may be any one of 1, 6, 10, 2, 30, 210. (The 
complementary factors will be 210, 35, 21, 140, 7, 1) 

Solution : There will be one switch NUMBER, with six positions 
1, 6, 10, 2, 30, 210. There will be six lamps corresponding 
to the possible complementary factors 210, 35, 21, 140, 7, 1. 



- 29 



A'-B 



142. LOGICAL NEGATION 

AvB ^---^A'vB' 









A 1 B f A'-B 1 A'vB' 1 JL 



144. LOGICAL EXCEPTION 






A B A' B 1 A-B' B-A' 1 



l 



- 30 - 



The circuit is exactly the same as the circuit for Logi- 
cal Negation because this problem has the same structure as 
that problem. 



144. LOGICAL EXCEPTION 

Problem : The logical operation of exception, as in the case 
of class F EXCEPT class G t is equal to the class every member 
of which is a member of F but is not a member of G. The re- 
sult of F EXCEPT G is equal to F-G 1 (read F dot G prime) mean- 
ing F AND NOT-G. 

Design a machine which will give the result of logical 
exception upon two classes, where either one may be 0, A, B f 1. 

Solution : There will be two switches, the FIRST CLASS F and 
the SECOND CLASS G. Each will have four positions, 0, A, B, 1. 
There will be eight lamps corresponding to the possible results 
0, A, B, A 1 , B\ AB\ B-A\ 1. The circuit appears in the 
diagram. 



145. MATCHING 

Problem : John Cullen has two sets of numbers 3, 6, 8, 9, 13, 
19 in one set, and 4, 7, 8, 10, 13, 17 in the other set. He 
wants a machine which will light a lamp if and only if the 
numbers set on each switch match each other. 

Solution : There will be two switches NUMBER OF FIRST SET and 
NUMBER OF SECOND SET. The positions of the first switch will 
be 3, 6, 8, 9, 13, 19. The positions of the second switch 
will be 4, 7, 8, 10, 13, 17. There will be one lamp, MATCHING. 
The circuit appears in the diagram. 



146. MERGING 

Problem : John Cullen has two sets of cards numbered 5, 6, 8, 
9 in one set and 4, 7, 8, 11 in the other set. He wants a 
machine which will tell him which set to choose from so that 
he can put his cards in exact numerical sequence from low 
number to high number, choosing from the first set in the case 
of a tie. 

Solution : There will be two switches CARD OF FIRST SET and 
CARD OF SECOND SET. The positions of the first switch will 
be 5, 6, 8, 9, and of the second switch will be 4, 7, 8, 11. 

- 31 - 



145. MATCHING 






Matching 



"X 



146. MERGING 




Choose 
From: 



First Set Second Set 



32 



There will be two lamps, one marked CHOOSE FROM THE FIRST SET 
and the other marked CHOOSE FROM THE SECOND SET. The circuit 
appears in the diagram. 



147. SELECTING 

Problem : John Cullen has two sets of numbers, the first set 
6, 8, 10, 12, 14 and the second set 9, 16, 25, 36, 49, and also 
a set of five sealed instructions numbered n = 1 to 5 which 
will tell him to select the _nth number of the first set or the 
nth number of the second set according to the instruction when 
he reads it. 

He wants a machine which will select the correct number 
according to the instruction when it is read. 

Solution : There will be two switches, one NUMBER OF SELECTION, 
with positions 1, 2, 3, 4, 5, and the other SEALED INSTRUCTION 
WHEN READ with two positions, SELECT FIRST NUMBER, and SELECT 
SECOND NUMBER. There will be ten lights 6, 8, 10, 12, 14 and 
9, 16, 25, 36, 49. 

The circuit appears in the diagram. 



148. THE MERRIMAC AND EASTERN TIMETABLE 

Problem : In the Merrimac and Eastern Railroad timetable, the 
following notes may or may not appear for any train: e, except 
Saturdays; s, runs Sundays only; m, last trip Nov. 11; k, Sat- 
urdays only; d, daily except Sundays; y, first trip Nov. 18. 
The railroad man making up the timetable, being human, may put 
down conflicting notes for the same train. 

Design a machine which will turn on an alarm for any 
conflicts. 

Solution : There will be six switches, labeled according to 
the notes above. Each switch will have two positions NO, YES. 
There will be one lamp: CONTRADICTION — ALARM. The conflict- 
ing combinations that the machine must report are es, ek, ed, 
sk, kd, my and any more complicated combinations such as esm. 
The circuit is shown in the diagram. 



- 33 - 



147. SELECTING 
10 r 




j\ Select Second Number 
*9 



Select First Number 



Number of Selection 



Sealed Instruction 
When Read 



6 8 10 12 14 9 16 25 36 49 J_ 



148. THE MERRIMAC AND EASTERN TIMETABLE 




Contradiction 
Alarm 



- 34 



149. THE THEATER SIGN "HAMLET" 

Problem : The manager of the Squamtick Theater has employed a 
stock company putting on Hamlet. He wants his marquee sign 
to show at successive times from 1 to 8, first H, then A, then 
M, then L, then E, then T, all shining in lights, all holding 
to the end and for another moment, and then all to go out. 

Design a machine for him. 

Solution : There will be one switch marked TIME, with posi- 
tions 1 to 8. There will be 6 lamps labeled H, A, M, L, E, T. 
The circuit is shown in the diagram. (Note that in this case 
we succeed in making an 8 position switch with six decks.) 



150. THE NEWS SIGN OF THE KALTROIT DISPATCH 

Problem : On August 9, 1958, the news sign of the Kaltroit- 
Dispatch is to show a certain message repeating in ten lights, 
each light lasting 6 seconds, and the next light coming on in 
3 seconds. The message is "Nautilus has crossed Pacific to 
Atlantic under North Pole icecap". 

Design the controlling circuit. 

Solution : There will be one switch TIME with positions 0, 
3 seconds, 6, 9, 12, and so on up to 33 seconds, and then re- 
peating. There will be ten lights, each one showing one of 
the ten words of the message. The circuit is shown in the 
diagram. 



151. A VARIATION OF NIM 

Problem : There are several ways of playing the game of Nim. 
One way is with two piles of matches, 15 in one pile, 12 in 
the other. The two players take turns. Each player must 
during his turn take one or more matches from any one pile 
(and may take the whole pile). The player taking the last 
match wins the game. 

Here is a sample game: 

(1) the player going first takes 9 from the 15 pile, 
leaving 6 

(2) the second player takes 10 from the 12 pile leav- 
ing 2 

(3) the first player takes 4 from the 6 pile leaving 2 



- 35 



149. THE THEATER SIGN "HAMLET" 




Time 



X 



H A M L E 

150. THE NEWS SIGN OF THE KALTROIT DISPATCH 
5 

\2 




( ft (ft (?)(?)(?)(£)(?)(?) (?) 0) 



Nautilus has crossed Pacific to Atlantic under North Pole icecap 

- 36 - 



1 



(4) the second player takes 1 from one of the two 2 
piles 

(5) the first player takes 1 from the other 2 pile 

(6) the second player must take 1 from one of the 1 
piles 

(7) the first player takes the last match from the 
other pile, and wins. 

The problem is to set up this way of playing Nim in a 
machine. The machine is to signal what move it makes in re- 
sponse to any position left by the human player. The machine 
is to accept any move by the human player, and is to signal 
unmistakably its own move. The machine is to play first or 
second. If the machine plays first, it should always win; if 
the machine plays second, it should win if the human player 
makes any mistakes. 

Design the machine. 

Solution : The circuit for the machine is shown in the diagram. 
It has three switches PILE A, PILE B, and WHOSE MOVE? To 
operate the machine, if it is the machine's move, set each 
switch at the number of matches in each pile. Then turn the 
WHOSE MOVE? switch to MACHINE'S. If the SIGNAL lamp is not 
lit, take the switch which is set at the larger number of 
matches, and turn it down until the lamp lights. This is the 
number of matches which should be left in that pile after the 
machine moves, and the machine takes from the pile the number 
of matches which will leave the number at which the switch is 
set. If the signal lamp is lit, the machine's move is to take 
one match from Pile A. 



37 



151. A VARIATION OF NIM 




Whose Move? 



Signal : This 4r 
is the Move 



38 - 



How To Go From 



R) < R ) 



Brainiacs and Geniacs 



To Automatic Computers 



Edmund C. Berkeley 



Copyright 1958 by Berkeley Enterprises, Inc. 



Published by Berkeley Enterprises, Inc. 
815 Washington St. 
Newtonville 60, Mass. 



First Printing, September 1958 



After a bright student or a resourceful teacher has worked for 
a while with Brainiacs (the word includes Geniacs and Tyniacs) the 
question inevitably comes up: "How do you go from these little semi- 
automatic machines to big automatic machines? What is the relation 
between these little electric brains and the giant brains?" These are 
important questions. 



1. The Nature of an Automatic Computer 

Perhaps the best way to answer these questions is to make 
clear the nature of an automatic computer, and explain the steps 
needed to go from a small machine of the electric brain (or Brainiac) 
type to a large and powerful electric brain. 

Automatic computers are of two main kinds, digital and analog . 
A digital computer handles information in the form of separate and 
distinct symbols, digits, letters, characters, yeses and noes. Its 
hardware has sharply different states, which may be for example 
the positions of a counter wheel marked 0, 1, 2, 3, and so on up to 
9, or the two positions "open" (or "O") and "shut" (or "1") of a two- 
position (or double-throw ) switch. An analog computer handles in- 
formation in the form of a magnitude of something physical that can 
vary, such as the position of a rod, the amount of rotation of a shaft, 
or a varying electrical voltage. 

All Brainiacs are digital. But if we should put a pointer on a 
Brainiac disc, mount it on a smooth shaft on which it could spin free- 
ly, and then spin it, and measure exactly where the pointer stopped, 
then we would be treating the disc as expressing the analog form of 
information. 

A digital computer can express letters as well as numbers; an 
analog computer can express numbers only. A digital computer can 
deal with numbers of 10 or 20 or more decimal digits; an analog com- 
puter can deal with numbers up to an accuracy of 4 or 5 significant 
figures at the most. A digital computer can handle almost any kind 
of mathematical or logical, business or scientific problem; an ana- 
log computer is nearly always limited to handling mathematical 
problems involving just one independent variable and up to 100 or 
more dependent variables. (If any of these phrases are not clear to 
you, we suggest that you look them up in a good algebra book. ) Both 
digital computers and analog computers are very useful, but usually 
in different areas. 

- 2 - 



Brainiacs are not related to analog computers; but they are 
closely related to digital computers. 

Nearly every automatic digital computer has identically the 
same basic logical design consisting of five units and two channels 
as shown in Figure 1. 



Control Line 




Infor- 



Storage Unit 

Or 
Memory Unit 




Control Line 



Arithmetic Unit 

Or 
Calculating Unit 



±3. 



Control Unit 



Figure 1 



The Basic Logical Design of an Automatic 
Digital Computer 



2. The Input Unit 

The input unit is the section of a computer where information 
is received from the outside world expressed in machine language, 
that is, expressed in the physical form which the machine can oper- 



ate with. In the case of a Brainiac, input is the setting oi a switch. 
In the case of a big computer, input may be punched paper tape, or 
punched cards, or magnetic tape (tape made of plastic impregnated 
with magnetic particles, and recorded on by producing a number 
of magnetically polarized spots, either polarized north-south or 
south-north). 

Different pieces of information are put into a Brainiac by man- 
ual changing of the position of a switch. Different pieces of input in- 
formation go into a big automatic computer by swift feeding of the 
tape or the cards through the machine, where the punched holes or 
magnetized spots are read by mechanical or electrical means. 



3. The Storage Unit 

The storage unit or memory unit of a computer consists of a 
large number of registers or locations where information is stored 
or remembered, available for reference by the computer when called 
for. 

An automatic computer may for example store information as 
polarized spots on the surface of a magnetic drum (a rotating cylin- 
der coated with a magnetic surface). When it is desired for the 
computer to refer to some information on the drum, the magnetic 
reading head associated with a certain path or channel around the 
drum is selected, and a certain time for reading is also selected, 
so that the pattern of l's and ! s contained in that information is 
piped out of the drum at that time. 

A Brainiac does not have a separate storage or memory unit. 
Its sorting or remembering of information is expressed in the posi- 
tion at which the switch has been set. 



4. The Arithmetic Unit 

The arithmetic unit or calculating unit of an automatic comput- 
er is the section of the machine where information is operated on ar- 
ithmetically or logically. The arithmetic unit is able to perform a 
number of different operations. Different signals for different oper- 
ations are sent to it, selecting addition, or subtraction, or multipli- 
cation, or division, or square root (in some computers), or compari- 
son, or selection, etc. ; and then this particular subprogram will be 



executed within the arithmetic unit, and then the result is given back 
to the rest of the machine. For example, if a multiplication is to be 
performed, this unit pays attention to the successive digits of the 
multiplier, and selects appropriate multiples of the multiplicand to 
be added and shifted accordingly. The arithmetic unit is almost a 
small computer by itself, but it operates with a fixed sequence of 
operations in order to perform multiplication. 

A number of the Brainiacs display this kind of behavior, sel- 
ection of the operation to be performed, for example, Brainiac No. 
L2, "A Simple Kalin-Burkhart Logical Truth Calculator", No. C6, 
"Operating With Infinity", and No. 125, "Turn Over and Turn Around' 1 

All the Brainiacs owe their chief interest to the fact that they 
display different kinds of rather efficient calculating circuits, cir- 
cuits typical of those that might appear in a special purpose digital 
computer. The circuits are often efficient because the Brainiacs 
make use of a novel and powerful kind of multiple switch, which can 
be assembled to make many, many varieties of calculating and rea- 
soning circuits. 

A big automatic computer on the other hand accomplishes cal- 
culating and reasoning by means of a small number of fundamental 
operations built into the arithmetic or calculating unit, which are 
then programmed in sequences to solve many very different kinds of 
problems. 



5. The Output Unit 

The output unit of a computer is the section of the computer 
where information is given back to the outside world, usually con- 
verted into forms that can be read easily by human beings, such as 
printed characters on paper. One way in which many automatic com- 
puters give back information is by means of an electric typewriter; 
the keys of this typewriter are driven by successive impulses de- 
rived from the computer, and a message is put out which can be 
read by human beings. 

A Brainiac always puts out its information in the form of the 
lighting or not lighting of lamps. This enables human beings to see 
what answers are denoted. Even big automatic computers have some 
lamps — usually a green lamp lighted for good operation, and red 
lamps for trouble, and frequently signal lamps indicating what parts 
of the machine require attention. 

- 5 - 



6. The Control Unit, Etc. 

The control unit of an automatic computer is the part of the 
machine which controls the switches or gates that connect specific 
registers in the various units Lo the information line; in this way it 
controls the sequence of operations in the computer, by means of a 
program of instructions or commands given to the machine in mach- 
ine language. 

A Brainiac has no control unit outside the human being who 
chooses to turn the switches to express different situations. 

The information line of an automatic computer is a channel, 
usually of one or more wires along which information flows through 
the computer in the form of a pattern of signals. 

An information line is present in a Brainiac. This is the wir- 
ing on the back of the panel. Information in the form of the presence 
or absence of electric current from the battery to the lights flows 
along a Brainiac ! s information channel. 

The control line of an automatic computer is the channel, usual- 
ly a single wire, along which the successive control signals flow, op- 
ening or shutting switches or gates. 

Since a Brainiac has no control unit, aside from the human be- 
ing who turns its switches, it has no control line, aside from the 
arms and hands of the human being who turns its switches. 



7. The Steps Needed to Convert a Brainiac 
into a Small Simple Automatic Computer 

What would be needed to convert a Brainiac into a very simple 
(and undoubtedly slow) automatic computer? 

First, the machine would need something that would enable it 
to operate different circuits at different times, completing a cycle 
of say 10 or 20 successive operations of circuits, and then repeating. 
Examples of Brainiac s that indicate how a stepping switch would op- 
erate are No. M2, "The Sign That Spells Alice", and No. Q6, "The 
Missionaries and the Cannibals". But the stepping switch for a more 
advanced machine should be self -moving, provided with a motor. 

- 6 - 



Second, the machine would need something that would enable it 
to store in a register information that might change from time to 
time. One of the simplest forms this could take would be an electrical 
relay; this is simply a switch with two positions, of which the leaf (or 
transfer contact) is normally pulled into one position by a spring, but 
may be pulled into the other position by magnetizing a piece of iron 
by running electric current through a coil around it (an electro-mag- 
net) . A relay will thus store or remember one binary digit of in- 
formation, 1 corresponding to the energized position, correspond- 
ing to the unenergized position. But a relay is expensive, costing 
50 cents to $2 for each changeable binary digit; and it is also slow, 
requiring on the order of a hundredth of a second to go from one po- 
sition to the other. For this reason, big automatic computers use 
for storage mainly polarized spots on magnetic surfaces. 

Third, the machine would need something for taking in a se- 
quence of pieces of information and instructions. One of the simplest 
forms for this would be a paper tape feed that would feed five hole 
paper tape. 

Fourth, as soon as we had made these three changes, we could 
no longer operate the machine on one flashlight battery. So we would 
have to have a power supply: this could be in the form of a 24 volt 
D, C. power supply, which could be operated through a transformer 
from a wall outlet of 110 volts A. C. 



8. Simon 

As soon as these changes are made, we leave the class of a $20 
kit, and go into the class of $300 of parts bought or picked up second 
hand from radio and war surplus stores. There seems to be hardly 
any other way of going about it. 

The steps that have just been described have been carried out. 
A miniature automatic digital computer using a stepping switch, 129 
relays, and a five-hole paper tape feed has been made, and more 
than one of them. The first one was made in 1950, and was called 
Simon — it was the predecessor of the Brainiac kits. 

Simon was an effort we made to make a complete miniature 
automatic digital computer. It has- 16 registers which could store 
any one of the four numbers 00, 01, 10, and 11. It had nine opera- 
tions, addition with and without carry, negation, greater than, selec- 

-7 - 



tion, and some more operations. The five -hole punched paper tape 
contained the given numbers presented at the start of the problem 
and a sequence of instructions for combining them. Simon appeared 
on the front cover of and was described in "Scientific American",' 
November, 1950, and "Radio Electronics", October, 1950. Over 400 
sets of Simon plans have been sold, and several other Simons have 
been constructed. 

The biggest drawback to Simon was its very small storage or 
memory, amounting only to 16 registers of 2 binary digits. So Simon 
was not able to compute its own instructions or store them internally. 
The part of the information line (see Figure 1) that goes into the con- 
trol unit was not present in Simon. However at present writing we 
have an operating magnetic drum memory (we call it Magdum; cost, 
$3000, vintage, 1957) of 128 registers of 4 binary digits. Our task 
currently is to hitch this memory on to Simon the small computer 
(vintage, 1950), so that Simon will be able to store instructions in- 
ternally and begin to be able to do useful work. 



9. Further Steps 

To come closer still to a complete and fast automatic digital 
computer — one that might be useful in calculations and in instruc- 
tion in a high school — much more money and labor are needed. The 
cost of electronic circuits to perform logical and arithmetical opera- 
tions is much greater than the cost of relay circuits. To trouble - 
shoot relay circuits requires $20 of simple apparatus and some com- 
mon sense. To troubleshoot electronic circuits requires a good 
oscilloscope, cost on the order of $500 to $800, and much more 
knowledge. 

Perhaps this situation will change for the better in the future. 
But in the meantime, simple switching circuits, such as the Brain- 
iacs, and simple equipment using relays, a stepper, and a tape feed, 
seem to be the main feasible solutions for studying automatic com- 
puters in the real, open to the bright student and the resourceful 
mathematics or science teacher. 



- 8 



BRAINIACS 



Small Electric Brain Machines 

Materials in the Kit and 
How To Assemble Them 

Edmund C. Berkeley 



(7^ 
Copyright ^ 1966 by Berkeley Enterprises, Inc. 



Published by Berkeley Enterprises, Inc. 
315 Washington St. , Newtonville, Mass. 02160 



First printing, January, 1966 



Introduction 

This report and the accompanying kit and literature present 
Brainiacs QO, sma ^ electric brain machines. Ihey are electrical 
machines which are able to calculate and reason automatically al- 
though they are too small to perform operations one after another ,. 
automatically. They show, with the least hardware that we have yet 
been able to work out that still allows interesting experiments, the 
fascinating power and variety of computing and reasoning circuits. 
There are over 200 experiments. 

Each of the machines uses one flashlight battery, not more 
than ten flashlight lamps, and not more than six multiple switches. 
All connections are made with nuts and bolts, and no soldering is 
required; the kit is completely safe. The kit, though inexpensive 
and convenient for constructing Brainiacs, is howeve'r not necessary; 
and some persons will prefer to construct their Brainiacs using other 
materials. 

The descriptions of the experiments are contained in the book 
"Brainiacs — 201 Small Electric Brain Machines and How to Make 
Them". The first thing to do is to read carefully: 

Chapter 1 - Small Electric Brain Machines — Some 
Questions and Answers 

Chapter 2 - Circuits and Circuit Diagrams 
Then this manual should be read, since it describes the materials 
in the kit and how to assemble them. Then a simple experiment 
from the book should be selected, constructed, and tried. It would 
be sensible to choose experiment No. 1 on page 9, which is also 
shown in the first template. 

If you find that at first you have some difficulty in understand- 
ing all that is in this kit, TAKE YOUR TIME and think; make first 
the simpler machines; then try the more complicated ones. To make 
a machine that will reason and calculate you too must reason and cal- 
culate. 

We hope that you find the experiments and the kit interesting, 
entertaining and amusing, and that you will enjoy playing with the kit 
and entertaining your friends with the little machines that you make. 
Any comments, suggestions for new experiments, and corrections, 
will be gratefully received. We shall be glad to hear from you. 

Edmund C. Berkeley 

- 2 - 



MATERIALS IN THE KIT AND HOW TO ASSEMBLE THEM 

With the Brainiac Electric Brain Construction Kit anyone can 
put together the machines of the types described in the experiments 
(and many more besides), so that they will perform operations of 
reasoning and computing. 

The kit is harmless. It runs on one flashlight battery. Wires 
are connected by fastening them to the same nut and bolt and tighten- 
ing the connection by gripping them between two bolts. No heat or 
soldering iron is required. DO NOT CONNECT this kit or any part 
of it to any home or industrial electrical power outlet; you are likely 
to destroy the material, and you may hurt yourself. 

The kit is simple, but nevertheless it takes effort and work to 
put the material together to make a functioning electric brain. We 
urge you to take your time. If necessary, read the instructions sev- 
eral times. If the instructions are still not clear, read ahead and 
then return. 

1. Parts List. The kinds of parts contained in the kit are the 
following: 

Insulated wire 

Battery box 

Bulbs, flashlight, 1-1/2 volts 

Socket parts for flashlight bulbs, holding five together 

Short bolts, 6/32, 1/2 inch long 

Hexagonal nuts, 6/32, 1/4 inch diameter 

Spintite blade 

Panel, masonite, rectangular, punched 

Multiple Switch Discs, masonite, circular, punched 

Long bolts, 6/32, 7/8 inch, for center pivot, etc. 

Washers, hard, cardboard 

Washers, soft, sponge rubber 

Jumpers, metal, brass 

Wipers, phosphor bronze 

In addition an ordinary size I) flashlight battery, I 1/2 volt, is needed 

Each of these items will now be described. (Note- J'ru,. - l to 
13 are not in this manual but in the book "Brainiacs^d sh"ouW be 
studied before the Figures in this manual are studied. ) 

- 3 - 



2. Wire. r lhe kit provides a coil of wire covered with in- 
sulation. This is like the wire connecting a lamp to a wall plug, 
for example, but adapted for handling a much smaller amount of 
electricity. Also, instead of two wires together making two paths 
for electricity, here is one wire only. In the Brainiac wiring that 
you will do, the wire follows a single path running from one end of 
the battery through some kind of loop to the other end of the battery, 
thus making a complete circuit. 

Your wire needs to be cut apart with a cutting pliers into 
pieces. A convenient length for many pieces is 18 inches, but some 
pieces can be shorter, about 8 inches long. About 3/4 of an inch of 
Insulation should be removed at each end of each piece. You can 
trim this off neatly with a dull knife. Also, a small amount of wire 
should be stripped of insulation and cut into pieces about 2 inches 
long. Ihese pieces of bare wire make transfer contacts, as will 
be explained later. 

3. Battery . An ordinary flashlight battery, size D, provides 
about 1 and l/2 volts. A volt is a unit of electric pressure or 
electric potential. A battery acts like a pump, and pumps electric- 
ity from one end of the battery around a circuit to the other end of 
the battery. A flow of electricity is an electric current . The fila- 
ment of a bulb through which the electricity flows provides a 
narrowness or a restriction or a resistance to the flow, so that it 
heats up and glows with "friction" as electricity flows through it. 

4. Battery Box . The battery box consists of a scored, glued 
piece of cardboard which will readily fold into a box of the right 
size to hold the battery. At each end of the box is a small hole. 
Through this hole from the inside of the box insert a bolt (on which 
a washer has been threaded, see Figure 15); then fasten the bolt 



Bare wire 



Insulated 
wire 



/ 




3olt f 
2 Nuts 



y\ 



7^ 



washer 



,Washer 



Battery in Box 




Box 



figure 15 
_ 4 _ 



with a nut on the outside of the box. Ihe battery terminal connect- 
ion is fastened to the projecting bolt with a second nut. Ihe box 
will now hold a battery snugly, giving good contact. The battery 
box may be tied securely to the panel with a tight string around it 
and passing through holes in the panel. 

5. Bulbs. You have small flashlight bulbs in the kit. Ihey 
will glow from a single flashlight battery. In order to make them 
light, you have to run one wire from the bottom metal plate of the 
battery to the side of the bulb, and another wire from the top of the 
flashlight battery to the center of the base of the bulb. Your conn- 
ections must be clean, not oily, nor corroded. Examine your 
bulbs closely from time to time to make sure that the filament, the 
little slender wire that you see inside the glass bulb, is all in one 
piece. If it is broken, the bulb is spoiled. 

6. Socket Parts. You have two "socket parts" for flashlight 
lamps. Each holds five lamps, in such a way that they can be 
screwed in and out of their socket holes. Views of the top, side 
and end of the socket part are shown in Figure 16. 



Top 
^iew 


• B O c O c O c OcO ? 






Side 
lew 





End 
View 

Figure 16 — Views of Socket Part 

In order to make use of this part actually assembled in a 
machine (see Figure 17), first, short bolts (for electrical connec- 
tions to the individual bulbs) are placed in the panel an inch apart 
and fastened tightly with nuts (see A in Figure 17). 

Second, long bolts for fastening the socket part to the panel 
are passed (1) through the two small holes at the two ends (see B 
in both figures) of the socket part, and (2) through the panel, and 
fastened tightly with nuts. Third, the bulbs are screwed through 
the large holes in the top of the socket part (see C in Figure 16), 
and screwed down far enough to make tight, snug contact with the 

- 5 - 



bolt under the bulb. Since the socket part is metal, one wire con- 
nector attached to the end bolt connects all the bulbs together to one 
side of the battery (see D in Figure 17). Then the screw at the base 
of each bulb enables it to be connected to its separate source of il- 
lumination from the circuit (see E in Figure 17). 



i^V 



B Q Q Q Q Q B 



£3 (side view, but side 
% is cut away) 



¥ ¥ A SS£^ A ^ A "ff^^ D connector to 

second ^^ ▼ b"^ one side of 

nut battery 

Figure 17 — Assembled Socket Part 



7. Nuts and Bolts . For fastenings, connections, and termin- 
als, here and there all over the machine, you have a supply of bolts 
and a supply of nuts. The nuts and bolts are of rust-proofed 
steel, and give good electrical connections. A bolt is inserted 
through any hole; then a nut is screwed down tight on the bolt holding 
it in position; then the connecting wire is wound around the end of 
the bolt coming through; then a second nut is screwed down tight on 
the wire and the bolt so as to give a tight electrical contact. 

8. Spintite Blade . In order to fasten your nuts and bolts easily, 
you will need a small screwdriver, which will fit in the slot of the bolt 
and enable it to be turned. You also have in the kit a small piece of 
hexagonal tubing (a spintite blade ) which fits over and grips the hexa- 
gonal bolt and enables it to be spun quickly down the shaft of the bolt, 
and tightened, with the screwdriver holding the bolt. 

9. Panel. In order to assemble your materials together into 
a machine, you have a rectangular panel consisting of masonite (thin 
pressed fiberboard). It contains holes for nuts and bolts so that the 
various parts of the set may be mounted together and assembled 
firmly. 

If you examine the panel, you will see two patterns of holes. 
One pattern (see Figure 18) consists of 102 holes arranged in sev- 
eral rows through the middle of the panel from end to end. 



Figure 18 

In this set of holes, all the hardware of a Brainiac machine is 
mounted except the "multiple switches", which will be explained 
in a moment. The second pattern consists of four rosettes of 65 
holes in a circular arrangement (see Figure 19). These are the 
"bases" of the multiple switches. 



"^^v? 




Pointer 


O ^v 


arrowhead 


>v 

o ^ 


Spoke 2 showing / 


o 


\ position / 


° 

o o 


\ of disc / 


> ° o o 


\ Spoke 1 / 


O 




Central ° 


\ / 


Pivot Hole ° 


1 




O o o o 

T?iTirr. TOO 


f> 


Spoke 



10 



14 



Figure 19 — Pattern of holes in the multiple switch 

(either the "base" in the panel or the "top", 
which is the disc). Also, the system of 
naming the holes. 



10. Multiple Switches. The remaining material provided in 
the kit consists of round pieces of masonite, each containing 65 holes 



- 7 



in the same circular arrangement (see Figure 19), and the hardware 
for assembling them into multiple switches, switches which are able 
to switch many circuits at the same time. Each of the circular 
pieces of masonite is about 4-3/8 inches in diameter, is illustrated 
in Figure 19, and is called a multiple switch top , or switch disc, ., 
or switch dial , or simply a disc . These multiple switches have 
been patented (2848568). 

In the panel each of the exactly similar sets of 65 holes is 
called a multiple switch base. In an early stage of design, the 
switch bases were separate pieces of masonite; but then it became 
evident that mounting of the hardware to make a machine would be 
better accomplished by having all the switch bases solidly connec- 
ted together in the panel. 

The top of a switch is fastened to the base of a switch by means 
of a center pivot , consisting of a long bolt, some hard washers, a 
sponge rubber washer, and a nut; the assembly of the center pivot 
is shown in Figure 20. 



I 



/~v 



Pivot bolt (long bolt), head 

Switch top 

Some hard washers 

Switch base, or panel 






i- 



- Sponge rubber washer 
-Another hard washer 



•Nut 

■ Pivot bolt, shaft 



Figure 20 — Center Pivot Assembly 



Instead of individual sponge rubber washers, the kit contains 
a small piece of sheet sponge rubber out of which the individual 
washers may be cut with a scissors. Cut out each rubber washer 
to be about the same size as one of the steel washers. Cut or poke 
a small hole in the middle of washer to allow a bolt to go through it. 
It is then ready for use; it functions as a compression spring. 



The holes (except the center hole) in each switch base and 



switch top are arranged in 4 rings and 16 spokes. The rings are 
called Ring 1, 2, 3, 4 going outward, and the spokes are called 
Spoke 0, 1, 2, 3, and so on around, to Spoke 15. The counting 
starts with the spoke directly to the right, and goes counterclock- 
wise. See Figure 19. 

Each of the holes in the switch base may or may not contain 
a short bolt, called a terminal, for making connections. The con- 
nections are made using two nuts, one for fastening the bolt sec- 
urely to the switch base, and the second for holding and tightening 
a wire around the bolt so as to make a good electrical connection 
with the bolt (see Figure 21). 



Terminal bolt (short bolt), " Wiper ' bent ' rid S eS up 




■ Switch base 
First small nut- 



*~Bare wire, looped 
tightly around 



Connector •— ^ T V^ 



Second nut 



Figure 21 — Assembly of Wiper, Terminal Bolt, and 
a Wire Connector 



11. Jumpers . Each pair of holes in a switch top, from Ring 
1 to Ring 2 or from Ring 3 to Ring 4 (or very rarely from Ring 2 to 
Ring 3) may or may not contain a jumper , a small piece of brass 
plated metal with two prongs, as shown in Figure 22. The two 
prongs fit into holes in the switch disc and are pressed down, like 
a clasp or T fastener, as shown in Figure 23. A jumper serves to 
make and break electrical contact as the switch is turned. 



Jumper prongs 




■ Jumper body ■ 
Side view End view 

Figure 22 — Jumper, not mounted 



-Jumper prongs bent down 



Switch top 



^=r 



Jumper body 

Side view End view 

Figure 23 — Jumper, inserted in two adjacent holes along a spoke 

12. Wipers . In between the jumper and the bolt, in the assem- 
* bled multiple switch, is inserted a wiper, a springy piece of phosphor 
bronze with a hole and two small ridges. The shape of the wiper un- 
bent, as it comes in the small envelope, is shown in Figure 24. The 
purpose of the wiper is to improve the electrical contact between the 
top of the switch (the disc containing the jumpers) and the bottom of 
the switch (the panel containing the bolts and nuts for the terminals). 
These wipers have been patented (2848568). 



Hole 



A' 




Wiper, ridges down 
Top view End view 

Figure 24 — Unbent wiper 



Ridges of 
wiper 



_V^. 



— disc 
.jumper 



Valley 



wiper ^T^Z^ s^$t~ w iper bent 
bent ^ *=;* 

-^ panel 



7$ 




Side view End view 

Figure 25 — Assembly of wipers 



10 - 



The way in which the wiper is assembled is shown in Figure 
25, and is as follows: (1) thread the bolt through the wiper, with 
its ridges down; (2) fasten the bolt not too tightly to the panel; 
(3) align the wiper with the spoke (or radius) of the switch; (4) now 
fasten the bolt tightly; (5) bend the wiper gently upwards and over 
the bolt, with the ridges up, in such a way that the wiper will slide 
neatly on the jumper, resting in its valley between the ridges; 
(6) assemble the multiple switch with (probably three) washers in 
between the disc and the panel; (7) adjust the amount of bending the 
wipers so that they push up and down nicely against the jumpers as 
the switch turns. 

For multiple switches with only two jumpers evenly spaced, 
or only three jumpers almost evenly spaced, you will not need wip- 
ers and should not use them, for such switches will work entirely 
properly without wipers. In these cases, you will need to make 
sure that the slots in the heads of the bolts are lined up with the 
spoke, so that the jumpers themselves will position (or detent ) 
along the spoke right above the bolts. (In assembling a switch with- 
out wipers, you need only one or two spacing washers along the 
center bolt, not three. ) For switches with four or more jumpers, 
you will need wipers, for otherwise the switch is likely to work 
unreliably. 

13. Assembly of the Multiple Switches. Before any of the 
multiple switches can function, however, it must first be assem- 
bled. 

Into the base we have to insert a number of nuts and bolts to 
hold wire connections and wipers. Just where these are inserted 
depends on the type of switch we desire to construct, two-position , 
or four -position, or some other type. 

Into the top of the switch we must insert a number of jumpers 
in order to make and break contacts. Each jumper is inserted along 
a spoke between one ring and the next. Just where the jumpers are 
inserted again depends on the type of switch we desire to construct. 

In order for the switch to stay in a position to which it is 
turned, the body of the jumper must line up with the valleys between 
the ridges on the wipers, and these valleys must be in line with the 
spoke; then the jumpers will have a tendency to catch in the valleys, 
as they should, to hold the switch in position (see Figure 25, end 
view). 

- 11 - 



Note that in some drawings of the multiple switches, the 
rings and spokes are drawn as thin lines; these lines are not ac- 
tually drawn on the switch discs nor the switch bases; nor do they 
represent electrical lines connecting terminals; instead they are 
drawn to make the arrangement clearer. 




Figure 26 — Three position switch, six decks (or poles or levels) 



Now suppose we wanted to assemble a switch which would 
have any one of three positions A, B, and C, and which would be 
capable of switching every one of six different circuits. A way in 
which that switch could be assembled is shown in Figure 26, in 
which both the top and the bottom of the switch are drawn over each 
other. Six jumpers are inserted in the top of the switch, shown as 
V////A in Figure 26. It is important that jumpers ordinarily be 
inserted in pairs opposite each other, for reasons of mechanical 
balancing, so that the top of the switch will stay parallel to the 
bottom of the switch. A total of six times six or 36 nuts and bolts 
are inserted in the bottom of the switch, in the spots marked # 



- 12 



in Figure 26. They are in groups of six called decks (also called 
poles, or levels); these decks are electrically independent, and they 
enable us to switch 6 different circuits. In the base, the bolts be- 
longing in any one deck in Ring 1 or Ring 3 are connected together 
by wire, as shown by the heavy line; they may be connected with one 
of the short wires 1-1/2 inches long. They are made electrically 
common; in other words, they are commoned. Together they con- 
stitute what is called a transfer contact . 

Let us now consider the layout of the spokes and the rings and 
the 64 holes which they produce. We can see that we can assemble 
a switch in a number of different ways. This is the advantage of 
the design of the multiple switch we have chosen (patent 2848568). 
Here are the types of switches (hat can be made with these parts: 





Maximum 


Number of Positions 


Number of Decks 


2 


16 


3 


10 


4 


8 


5 


6 


6 to 8 


4 


9 to 16 


2 



If nuts and bolts did not cost anything, we could insert 64 nuts 
and bolts into the base of each switch and leave them there — ready 
for use in any switch. Actually, because the kit has a limited supply, 
it may be necessary to move nuts and bolts from one switch to another 
in order to make the different machines we want. 

In the case of jumpers and wipers, we shall fairly often have to 
move them to different places, in order to make different switches 
for different machines. 

14. Additional Material . You may obtain additional or replace- 
ment material for this kit by buying it at a local store, or by writing 

to us. Obviously, if your battery runs down, or if you want more wire, 
or if you want more nuts and bolts, the easy thing to do is to buy them 
in your neighborhood. But for more switch discs or more jumpers, 
etc. , you will probably need to write us. Prices for these items are 
listed on a price list enclosed with the kit or obtainable on request. 

15. Labels. The best procedure for making labels is: (1) type 
them out or write them out neatly on paper; (2) cut them out; (3) fasten 

- 13 - 



them on the board with cellophane tape. 

16. Templates . In work with electrical circuits we need to 
lay out beforehand what we are going to do. We need to design on 
paper how we are to connect the different pieces of material. For 
this purpose, we use circuit diagrams, wiring lists, and templates^ 

A circuit diagram , as mentioned before, shows the scheme of 
connection of batteries, switches, lights, etc., in order to make the 
circuit. In a circuit diagram we pay little attention to the actual phy- 
sical location of the material; we just show a diagram of its arrange- 
ment. 

In a wiring list , we name the terminals, by words or letters or 
numbers, and we state, for every part of the circuit, what terminal 
is connected to what terminal. In a wiring list again we pay no atten- 
tion to the actual spatial locations of the terminals. For example, if 
without drawing the wire, we write M to. . . M , we are using the prin- 
ciple of a wiring list. 

In a template , the case is different; we show the actual wiring 
and the approximate relative spatial location of the different pieces 
of material used in the circuit. In other words, we draw an accur- 
ate geographical map of where the terminals are, and then we indic- 
ate the wiring either by drawing lines for the connections or by writ- 
ing notes showing the connections. For some illustrative Brainiac 
experiments, templates on a reduced scale are included in the kit. 

In each experiment in the Brainiac kit, the important part of 
the wiring is on the rear side of the panel. Accordingly, each tem- 
plate shows a scaled picture of the rear of the panel. It is there- 
fore a mirror image: what is on the right in the drawing in the man- 
ual is on the left in the template; and vice versa. Of course, some 
of the information appearing on the template belongs on the front side 
of the board: the labels of the switches, their positions, and the 
lights; and the location of the jumpers in the discs. If one pays care- 
ful attention to the two drawings, one in the manual and one in the 
template, the way the hardware and labels actually are arranged 
should become quite clear. 

17. Trouble -Shooting. After you have wired up a machine, 
and start to play with it, you are likely to find that it does not work 
entirely correctly. All engineers worth their salt who do any kind 
of significant work with electrical circuits discover when they first 

- 14 - 



assemble a new piece of equipment that it does not work properly. 
Finding out the reasons why and removing the causes of malfunction- 
ing, the process known as trouble-shooting , therefore, is an import- 
ant and essential part of making any piece of equipment start working 
and stay working; and good trouble- shooting is the mark of a good 
engineer. 

In order to trouble-shoot, it is helpful to have a systematic 
and logical checklist of questions to be answered one after another, 
and in addition testing apparatus which will tell whether a part of a 
circuit actually does what it is supposed to do. In order to test mach- 
ines made with a Brainiac kit, the essential piece of testing apparatus 
is what is called a continuity tester . A simple form of such a tester 
is a flashlight battery, a lamp, and two wires with bare ends, conn- 
ected as shown in Figure 27. Then, when you take the ends of the 
two wires, and touch a certain pair of terminals, if you obtain a 
light, you know that that part of the circuit is connected, is contin- 
uous; while if you obtain no light, you know that that part of the cir- 
cuit is not connected, is isolated. Then, you compare what your 
tester shows to be actual fact with what you are supposed to have 
according to the circuit diagram, and you have either verified the 
correctness of that part of the circuit, or located some trouble. 

Here are some checklist questions which make a beginning at 
trouble -shooting: 

(1) Does each wire actually make contact with each 

terminal to which it is fastened? 

(2) Does each jumper actually make contact with the 

wiper at each terminal, as its switch turns? 

(3) Does each lamp really light? 

(4) Is there electricity in the battery? 

(5) Has any wire broken inside its insulation? 

(6) Is there a mistake or typographic error in the 

diagram or the instructions? (This question 
must always be asked, because no author or 
printer is infallible. ) 

(7) Does each wire go where it should? 

(8) Has each label been fastened on in its right place? 

(9) Is each jumper in its right place? 
(10) Is each terminal in its right place? 



15 




H I 



Figure 27 — Continuity Tester 



If you can locate and remove trouble skillfully, you can be well 
satisfied with what you have learned. 

18. Design for a Stand . When working on wiring and assemb- 
ling a Brainiac machine, it is convenient to make a simple stand for 
holding the panel upright, so that you can work on both sides. Here 
is a design for a stand which will do this. 

1. Take two pieces of rectangular wooden rod about 1 inch by 
1 inch by 9 Inches long: 

Narrow Slot 
(^ (drawn exaggerated) 




Figure 28 



2. Saw a slot in the center of each piece of rod about 2/3 of the 
way through. 

3. With a file, widen and rub down the sides of the slot so that 
the Brainiac panel fits into the slot snugly, but not too tightly nor too 
loosely. 

4. Then for wiring, assembling, displaying, etc. , the panel, 
held in the stand, looks like: 



Figure 29 



- 16 



Brainiacs — 



Small Electric Brain Machines 

Introduction and 
Explanation 

Edmund C. Berkeley 



Copyright w 1959 by Berkeley Enterprises, Inc. 



Published by Berkeley Enterprises, Inc. 
815 Washington St. , Newtonville 60, Mass. 



First printing, April, 1959 



P59 



Introduction 

This report and the accompanying kit and literature present 
BrainiacsQP, small electric brain machines. They are electrical 
machines which are able to calculate and reason automatically al- " 
though they are too small to perform operations one after another 
automatically. They show, with the least hardware that we have yet 
been able to work out that still allows interesting experiments, the 
fascinating power and variety of computing and reasoning circuits. 

The experiments, at present writing amounting to over 150, 
are described in other publications included in this kit. This report 
is devoted to introducing and explaining Brainiacs, "Brainy Almost- 
Automatic Computers". 

Each of the machines uses one flashlight battery, not more 
than ten flashlight lamps, and not more than six multiple switches. 
All connections are made with nuts and bolts, and no soldering is 
required; the kit is completely safe. The kit, though inexpensive 
and convenient for constructing Brainiacs, is however not necessary; 
and some persons will prefer to construct their Brainiacs using other 
materials. 

We hope that you find the experiments and the kit interesting, 
entertaining and amusing, and that you will enjoy playing with the kit 
and entertaining your friends with the little machines that you make. 

If you find that at first you have some difficulty in understand- 
ing all that is in this kit, TAKE YOUR TIME and think; make first 
the simpler machines; then try the more complicated ones. To make 
a machine that will reason and calculate you too must reason and cal- 
culate. 

Any comments, suggestions for new experiments, and correc- 
tions, will be gratefully received. We shall be glad to hear from you. 

Edmund C. Berkeley 



-2 - 



BRAINIACS — 

Small Electric Brain Machines — 

INTRODUCTION AND EXPLANATION 

Table of Contents 

Title Page 

1. General Information 4 

2. Circuits 6 

Circuit Diagrams 6 

Battery 9 

Switches 9 

Decks 9 

3. Materials in the Kit, and Explanation of Them 10 

Battery Clamp 12 

Bulbs 13 

Socket Parts 13 

Panel 14 

Multiple Switches 15 

Jumpers 17 

Wipers 18 

Assembly of the Multiple Switches 19 

Templates and Circuit Diagrams 22 

Trouble -Shooting 22 

Continuity Tester 24 

Design for a Stand 24 



3 - 



Section 1. General Information 

Question : What is an "electric brain machine"? 

Answer: An electric brain machine is a machine containing el- u 
ectric circuits which is able to calculate or reason automatically. 
The bigger electric brains are able to carry* out long sequences of 
reasoning and calculating operations, thus solving complex problems. 
Such a machine is a true "electric brain machine", for there is no 
doubt that until such operations began to be done by machines, every- 
one agreed that such operations constituted thinking and were charac- 
teristically the operations carried out by brains. 

The first modern electric brain machine was finished at 
Harvard University in 1944, and has been working there ever since. 
Now thousands of such machines are in existence, and at work pro- 
ducing knowledge. This development is so important that it is often 
called the "Second Industrial Revolution". 

Question: What is a BRAINIAC? 

Answer : A BRAINIAC is an electric brain machine which is 
small. If expense were no barrier, we could make one using only a 
small amount of hardware which would run extremely well doing 
many kinds of problems. But expense of course is a barrier, and the 
small electric brain machines which we talk about in this report 
are machines which are made of multiple switches, a panel for 
mounting them, a flashlight battery, flashlight bulbs, nuts, bolts, 
and other hardware. The electric brain machines we talk about 
here will not run by themselves; that is, whenever the machine is 
supposed to do something, you yourself have to turn the switch re- 
presenting the machine's action. But nevertheless these machines 
do calculate and reason automatically, because the way that they 
are wired expresses the calculating and the reasoning. 

Question: What is the origin of the BRAINIAC S? 

Answer : Most of the Brainiacs (No. 34 and up) were cre- 
ated after December 25, 1955; the first 33 were designed earlier. 
All of them however are the outgrowth of work which we have 
been doing since 1946, and which is still continuing — the explora- 
tion of intelligent behavior expressed in machines. For this pur- 
pose, we maintain a small laboratory, and are continually working 



4 - 



on one phase or another of small robots and other machines which 
display intelligent behavior. Among other steps leading to the 
Brainiacs are the following. 

In 1950, for educational and lecturing purposes, we construc- 
ted a miniature electric brain called Simon. Although only 1-1/4 
cubic feet in size, and limited in capacity, it was a complete auto- 
matic computer, and it could show how a machine could do long se- 
quences of reasoning operations. The picture of Simon appeared on 
the front cover of two magazines, "Scientific American" and "Radio 
Electronics"; the machine itself was demonstrated in more than 
eight cities of the United States. Over 350 sets of Simon plans have 
been sold. But this machine costs over $300 for materials alone, 
and is therefore too expensive for many situations in playing and 
teaching. 

Soon after Simon was finished we began work to develop really 
inexpensive electric brains. By 1955, we had gathered and worked 
out descriptions of 33 small electric brain machines, which 
could be made with very simple electrical equipment. These mach- 
ines were incorporated in a construction kit, which would make any 
one of these little machines. The name of the kit was "Geniac Kit 
No. 1"; the word "Geniac" ® came from the phrase "Genius Al- 
most-Automatic Computer", and has been registered as a trade- 
mark. 

Question: How am I to understand the experiments? 

Answer: The first thing to do is not to rush, but to take your 
time, and read as carefully as you can all the general information. 
Read particularly this report which talks about circuits and how they 
work. The circuits which make these machines operate are all of 
them circuits in which electricity from a flashlight battery flows 
along wires and causes certain light bulbs to light up. The labels 
on the switches, on their positions, and on the lights show the mean- 
ing which is to be assigned. 

In the same way, in the pilot's cabin of an airplane, or on the 
operating panel of an oil refinery, the switches, the lights, the dials, 
and the labels tell the meaning of what is going on, so that the air- 
plane or the refinery can be controlled. 



5 - 



Question : How are the circuits like those in the experiments designed? 
I notice that each experiment is set up as a problem and solution: how 
would I be able to work out the solution for myself? 

Answer : This is an interesting and important subject, the design 
of switching circuits. If you find the subject really interesting and 
worth a lot of work, and want to do that work, then you are likely to 
be well qualified to be an electrical engineer or electronic engineer, 
or a designer of computing machines, and you may have an excellent 
professional future lying in front of you. 

An introduction to the design of switching circuits given in 
"Introduction to Boolean Algebra for Circuits and Switching" is in- 
cluded in the kit. This branch of knowledge, a new kind of algebra 
called Boolean algebra, is one of the best approaches. This is the 
algebra of AND, OR, NOT, EXCEPT, UNLESS, IF. . . THEN, IF 
AND ONLY IF, and some other very common words and expressions 
of language and logic. This algebra is a part of the subject called 
symbolic logic, and has an important application to any circuits that 
make use of circuit elements that can be either on or off, lighted or 
not lighted, conducting or not conducting, and so forth. 



Section 2. Circuits 

The small electric brain machines described in the kit are 
made of: a battery, or source of electric current; wires, which con- 
duct it; switches, which change the paths along which the current 
flows; lights, which show where the current is flowing; and other 
hardware, such as nuts and bolts, which enables the whole machine 
to function together. In all of these machines the current starts 
from one end of the battery and flows in a path or circuit that event- 
ually returns to the other side of the battery. 

Circuit Diagram. The diagram of the circuit or circuit diagram 
or circuit schematic shows the scheme of connection of the battery, 
the switches, and the lamps, in order that the machine will function 
as it is supposed to. The diagram does not necessarily show the phy- 
sical location of the hardware but only the arrangement of the connec- 
tions of the hardware. 

The symbols used in our circuit diagrams are shown in the 
accompanying figures. We need to pay attention only to a few kinds 
of hardware. 

- 6 - 



+ 



Source 



Fig. 1 . — Battery 



Ground 



Fig. 2 —Battery terminals, 
when separated 



j 



Fig. 3 — Wire, or conductor 



Fig. 4 — Wires joining or cross- 
ing with electrical connections 



<D 



Fig. 5 — Wires crossing with no 
electric connection 

Swinging Arm 
of Switch Contact 



Wire 



Wire 



Wire 



Fig. 7 — A Switch 



Fig. 6 —Lamp bulb 



Arm 



Hinge 



Two 
Contacts 



_J,.Hinge 



Two Contacts \ # -' 

Fig. 8 — Two -Position Switch 
(two ways of drawing it) 



( Note: The line of small dots associates the name with the part named.) 



Arm- 






Hinge 



Three 
Contacts 



Hinge 

Arm 



^ .Co 



Four 
Contacts 



Fig. 9 —Three -Position Switch Fig. 10 —Four-Position Switch 



Transfer s^ Transfer Contact 

Contact ^ic S 

Normally Normally ART 

Closed Open 

Contact Contact Contacts 

Figure 11 - 1 - Contacts, and their Possible Names 



T-l T-2 

Z-l / Z-2 



A-l B-l C-l A-2 B-2 C-2 A-3 B-3 C-3 A -4 B-4 ( 

Figure 12 — Four -Deck Three -Position Switch Z 
Drawn Schematically 




(Deck Z-2) a-2 

B-2 



A -3 



B-3 L 
(Deck Z-3) 




Figure 13 — Four- Deck Three-Position Switch Z 

Drawn Pictorially 



Battery . Fig. 1 is the diagram for a battery. The long and 
short lines supposedly represent the two kinds of plates in a battery 
by means of which the electric current is generated. The number of 
long and short lines does not symbolize anything, and does not have 
a special meaning. 

Instead of showing the two ends of the battery located next to 
each other, another method may be used (see Fig. 2). One end or 
pole of the battery may be shown at one place as a small letter "o" 
meaning "source of current". The other end or pole of the battery 
may be shown at another place with the symbol "_JL M meaning the 
"sink of current" or "ground". 

Wire . A line in a circuit diagram (see Fig. 3) represents an 
insulated wire, a connector from some point to some other point. 

Dots (see Fig. 4) represent points where electrical connections 
are established by fastening two wires together so current can flow 
easily between them. 

In Fig. 5, two wires cross (drawn in either one of two ways) but 
there is no electrical connection between them. One wire is actually 
either above or below the other. 

Lamps . The diagram of Fig. 6 sketches the glass bulb and the 
filament of the lamp. The two dots are its connections. 

Switches. A switch was originally a device for shifting a train 
from one track to another. Now in addition, it is a device for turn- 
ing an electric current from one path to another; see Fig. 7. 

In Fig. 8, 9, and 10, appear more abbreviated diagrams of 
switches; they are diagrams therefore easier to draw. 

Switch Contacts. In any switch, the contacts have names. See 
Fig. 11 for examples of switch contacts and their possible names. 

Decks . A single switch may be constructed having two or three 
or more electrically nonconnecting sections (often called decks or 
poles) so that as it is turned, it simultaneously switches two or 
three or more electrically independent paths. In circuit diagrams 
this property of a switch may be shown by using a name for the 
switch and numbers 1, 2, 3, etc. , for the decks. For example, a 



switch (named Z) with three positions (A, B, and C) and four decks 
(named 1, 2, 3, and 4) is diagrammed in Figure 12. 

Suppose however we actually wanted to make such a switch; it 
should have three positions and should enable us at one and the 
same time to shift four separate circuits. We could make it as shown 
in Figure 13. We could start with a flat round piece of non-conducting 
material. We could fasten jumping or bridging conductors along four 
radii in such a way that when we turn the switch at its central hinge 
or pivot, each jumper (drawn as Y/f/SA ) is shifted simultaneously and 
transfers current from its transfer points T to its corresponding con- 
tact points A, B, C. This idea is at the heart of the patented multiple 
switch used in the Brainiac, Tyniac, and Geniac kits. 

Examine the round discs in the kit. Each has a pattern of 65 
holes, a center hole for a hinge or pivot, and four rings of holes 
arranged along 16 spokes (or radii). With the hardware in the kit, 
we can assemble these discs to switch many different circuits. 



Section 3. Materials in the Kit, and Explanation of Them 

With the Brainiac Electric Brain Construction Kit anyone can 
put together the machines of the types described in the experiments 
(and many more besides), so that they will perform operations of 
reasoning and computing. 

The kit is harmless. It runs on one flashlight battery. Wires 
are connected by fastening them to the same nut and bolt and tighten- 
ing the connection by gripping them between two bolts. No heat or 
soldering iron is required. DO NOT CONNECT this kit or any part 
of it to any home or industrial electrical power outlet; you are likely 
to destroy the material, and you may hurt yourself. 

The kit is simple, but nevertheless it takes effort and work to 
put the material together to make a functioning electric brain. We 
urge you to take your time. If necessary, read the instructions sev- 
eral times. If the instructions are still not clear, read ahead and 
then return. 

1. Parts List. The kinds of parts contained in the kit are the 
following: 

Insulated wire 

Battery, dry cell, flashlight, 1-1/2 volts 

- 10 - 



Battery clamp with switch 

Bulbs, flashlight, 1-1/2 volts 

Socket parts for flashlight bulbs, holding five together 

Short bolts, 6/32, 1/2 inch long 

Hexagonal nuts, 6/32, 1/4 inch diameter 

Spintite blade 

Panel, masonite, rectangular, punched 

Multiple Switch Discs, masonite, circular, punched 

Long bolts, 6/32, 7/8 inch, for center pivot, etc. 

Washers, hard 

Washers, soft 

Jumpers, metal, brass 

Wipers, phosphor bronze 

Each of these items will now be described. 

2. Wire. The kit provides a coil of wire covered with insula- 
tion. This is like the wire which you will find connecting a lamp to a 
wall plug, or a telephone to the telephone box, but adapted for hand- 
ling much smaller currents and voltages. Instead of two wires wound 
together, here is one wire only. In the wiring that you will need to do, 
your two wires will be taken care of when you make for yourself a 
complete circuit, running from one end of the battery around some 
kind of loop to the other end of the battery. 

Your wire will need to be cut apart with a cutting pliers into 
lengths. A convenient length for much of the wire to oe cut into is 
18 inches, but some pieces can be shorter, about 8 inches long. 

About three quarters of an inch of the insulation will need to be 
trimmed off at each end of each piece. You can trim this off neatly 
with a dull knife; you should try to avoid cutting or nicking the wire 
since this will shorten the length of time it will last. 

A small amount of the wire should be stripped of insulation and 
cut into pieces 1 or 2 inches long. These pieces of bare wire will be 
used for making transfer contracts on the multiple switches, as will 
be explained later. 

3. Battery. This is an ordinary flashlight battery, of about one 
and a half volts. A volt is a unit of electric push, or electric press- 
ure, or electric potential. All these terms mean the same thing. 



- 11 



You can think of a battery as a pump, which is able to push el- 
ectrons, or little marbles of electricity, away from the plus end of 
the battery and towards the minus end of the battery, waiting for 
some kind of circuit at the minus end so that the electrons can flow 
around the circuit back to the plus end of the battery. A flow of el- 
ectrons is an electric current . 

The filament in the bulb through which the electrons flow pro- 
vides a resistance or restriction or narrowness for the flow of el- 
ectrons, so narrow in fact that it heats up and glows with friction 
as the electrons go through it. 

4. Battery Clamp and On-Off Switch . This consists of a metal 
clip that is fastened with nuts and bolts into the panel and which will 
grip your battery and hold it. You then can fasten connections to the 
battery clamp and yet snap out your battery when it is weak and snap 
in another stronger battery in place of it when you need to. 



" Switch handle 



Connect one wire here «. 




'Panel 



Connect other battery lead to mounting screw 
Figure 14 (Side View) 

Switch handle (rotates) 



Up: Off position 




Down: On position 



Panel 



Figure 15 (End View) 
- 12 - 



The battery clamp has attached to it an on-off switch. Make con- 
nections as illustrated in Figure 14. The machine is off when the 
switch handle is in the upright position. The machine is on when 
the handle is rotated 90 degrees (see Figure 15). 

5. Bulbs . You have small flashlight bulbs in the kit. They 
will glow from a single flashlight battery. In order to make them 
light, you have to run one wire from the bottom metal plate of the 
battery to the side of the bulb, and another wire from the top of the 
flashlight battery to the center of the base of the bulb. Your conn- 
ections must be clean, not oily, nor corroded. 

Examine your bulbs closely from time to time to make sure 
that the filament, the little slender wire that you see inside the 
glass bulb, is all in one piece. If it is broken, the bulb is spoiled. 

6. Socket Parts. You have two "socket parts" for flashlight 
lamps. Each holds five lamps, in such a way that they can be 
screwed in and out of their socket holes. Views of the top, side 
and end of the socket part are shown in Figure 16. 



Top 
View 


• B O c O c O c OcO ? 






Side 
/iew 





End 
View 

Figure 16 — Views of Socket Part 

In order to make use of this part actually assembled in a 
machine (see Figure 17), first, short bolts (for electrical connec- 
tions to the individual bulbs) are placed in the panel an inch apart 
and fastened tightly with nuts (see A in Figure 17). 

Second, long bolts for fastening the socket part to the panel 
are passed (1) through the two small holes at the two ends (see B 
in both figures) of the socket part, and (2) through the panel, and 
fastened tightly with nuts. Third, the bulbs are screwed through 
the large holes in the top of the socket part (see C in Figure 16), 
and screwed down far enough to make tight, snug contact with the 

- 13 - 



bolt under the bulb. Since the socket part is metal, one wire con- 
nector attached to the end bolt connects all the bulbs together to one 
side of the battery (see D in Figure 17). Then the screw at the base 
of each bulb enables it to be connected to its separate source of il- 
lumination from the circuit (see E in Figure 17). 



* q q a a q » 




£^(side view, but side 
is cut away) 



A^A ^A fA^ D connector to 

Tr one side of 

nut battery 

Figure 17 — Assembled Socket Part 



7. Nuts and Bolts . For fastenings, connections, and termin- 
als, here and there all over the machine, you have a supply of bolts 
and a supply of nuts. The nuts and bolts are of cadmium-plated 
steel, and give good electrical connections. A bolt is inserted 
through any hole; then a nut is screwed down tight on the bolt holding 
it in position; then the connecting wire is wound around the end of 
the bolt coming through; then a second nut is screwed down tight on 
the wire and the bolt so as to give a tight electrical contact. 

8. Spintite Blade . In order to fasten your nuts and bolts easily, 
you will need a small screwdriver, which will fit in the slot of the bolt 
and enable it to be turned. You also have in the kit a small piece of 
hexagonal tubing (a spintite blade ) which fits over and grips the hexa- 
gonal bolt and enables it to be spun quickly down the shaft of the bolt, 
and tightened, with the screwdriver holding the bolt. 

9. Panel. In order to assemble your materials together into 
a machine, you have a rectangular panel consisting of masonite (thin 
pressed fiberboard). It contains holes for nuts and bolts so that the 
various parts of the set may be mounted together and assembled 

firmly. 

If you examine the panel, you will see two patterns of holes. 
One pattern (see Figure 18) consists of 102 holes arranged in sev- 
eral rows through the middle of the panel from end to end. 



14 



Figure 18 

In this set of holes, all the hardware of a Brainiac machine is 
mounted except the "multiple switches", which will be explained 
in a moment. The second pattern consists of four rosettes of 65 
holes in a circular arrangement (see Figure 19). These are the 
"bases" of the multiple switches. 




Pointer 
arrowhead 
Spoke 2 showing 
position j 
of disc/ 
Spoke 1 



Spoke 



Figure 19 — Pattern of holes in the multiple switch 

(either the "base" in the panel or the "top", 
which is the disc). Also, the system of 
naming the holes. 



10. Multiple Switches. The remaining material provided in 
the kit consists of round pieces of masonite, each containing 65 holes 



- 15 - 



in the same circular arrangement (see Figure 19), and the hardware 
for assembling them into multiple switches, switches which are able 
to switch many circuits at the same time. Each of the circular 
pieces of masonite is about 4-3/8 inches in diameter, is illustrated 
in Figure 19, and is called a multiple switch top , or switch disc, ». 
or switch dial , or simply a disc . These multiple switches have 
been patented (2848568). 

In the panel each of the exactly similar sets of 65 holes is 
called a multiple switch base. In an early stage of design, the 
switch bases were separate pieces of masonite; but then it became 
evident that mounting of the hardware to make a machine would be 
better accomplished by having all the switch bases solidly connec- 
ted together in the panel. 

The top of a switch is fastened to the base of a switch by means 
of a center pivot , consisting of a long bolt, four hard washers, a 
sponge rubber washer, and a nut; the assembly of the center pivot 
is shown in Figure 20. 



£ 



^~V 



Pivot bolt (long bolt), head 



^SS^caJ 



Switch top 

Three hard washers 

Switch base, or panel 



Sponge rubber washer 
•Fourth hard washer 



■Nut 

- Pivot bolt, shaft 



Figure 20 — Center Pivot Assembly 



Instead of individual sponge rubber washers, the kit contains 
a small piece of sheet sponge rubber out of which the individual 
washers may be cut with a scissors. Cut out each rubber washer 
to be about the same size as one of the steel washers. Cut or poke 
a small hole in the middle of washer to allow a bolt to go through it. 
It is then ready for use; it functions as a compression spring. 

The holes (except the center hole) in each switch base and 



- 16 - 



switch top are arranged in 4 rings and 16 spokes. The rings are 
called Ring 1, 2, 3, 4 going outward, and the spokes are called 
Spoke 0, 1, 2, 3, and so on around, to Spoke 15. The counting 
starts with the spoke directly to the right, and goes counterclock- 
wise. See Figure 19. 

Each of the holes in the switch base may or may not contain 
a short bolt, called a terminal, for making connections. The con- 
nections are made using two nuts, one for fastening the bolt sec- 
urely to the switch base, and the second for holding and tightening 
a wire around the bolt so as to make a good electrical connection 
with the bolt (see Figure 21). 

Terminal bolt (short bolt) ^^~ Wiper ' bent ' rid * eS up 

^5*< Switch base 

First small nut- 

**~Bare wire, looped 
tightly around 

Connector — f ' ~~ *X^ Second nut 

Figure 21 — Assembly of Wiper, Terminal Bolt, and 
a Wire Connector 



11. Jumpers. Each pair of holes in a switch top, from Ring 
1 to Ring 2 or from Ring 3 to Ring 4 (or very rarely from Ring 2 to 
Ring 3) may or may not contain a jumper , a small piece of brass 
plated metal with two prongs, as shown in Figure 22. The two 
prongs fit into holes in the switch disc and are pressed down, like 
a clasp or T fastener, as shown in Figure 23. A jumper serves to 
make and break electrical contact as the switch is turned. 




Jumper prongs 




• Jumper body ■ 
Side view End view 

Figure 22 — Jumper, not mounted 



- 17 



-Jumper prongs bent down 



-E 



Switch top 



Jumper body 




Side view End view 

Figure 23 — Jumper, inserted in two adjacent holes along a spoke 

12. Wipers . In between the jumper and the bolt, in the assem- 
bled multiple switch, is inserted a wiper, a springy piece of phosphor 
bronze with a hole and two small ridges. The shape jof the wiper un- 
bent, as it comes in the small envelope, is shown in Figure 24. The 
purpose of the wiper is to improve the electrical contact between the 
top of the switch (the disc containing the jumpers) and the bottom of 
the switch (the panel containing the bolts and nuts for the terminals). 
These wipers have been patented (2848568). 

Hole 



® 




Wiper, ridges down 
Top view End view 

Figure 24 — Unbent wiper 



Ridges of 
wiper 



wiper ^-yC >£- 

bent ^ 



disc 
.jumper 
wiper bent 

-^ panel 




Valley 
of wiper 

-bolt 



Side view End view 

Figure 25 — Assembly of wipers 



18 - 



The way in which the wiper is assembled is shown in Figure 
25, and is as follows: (1) thread the bolt through the wiper, with 
its ridges down; (2) fasten the bolt not too tightly to the panel; 
(3) align the wiper with the spoke (or radius) of the switch; (4) now 
fasten the bolt tightly; (5) bend the wiper gently upwards and over 
the bolt, with the ridges up, in such a way that the wiper will slide 
neatly on the jumper, resting in its valley between the ridges; 
(6) assemble the multiple switch with (probably three) washers in 
between the disc and the panel; (7) adjust the amount of bending the 
wipers so that they push up and down nicely against the jumpers as 
the switch turns. 

For multiple switches with only two jumpers evenly spaced, 
or only three jumpers almost evenly spaced, you will not need wip- 
ers and should not use them, for such switches will work entirely 
properly without wipers. In these cases, you will need to make 
sure that the slots in the heads of the bolts are lined up with the 
spoke, so that the jumpers themselves will position (or detent ) 
along the spoke right above the bolts. (In assembling a switch with- 
out wipers, you need only one or two spacing washers along the 
center bolt, not three. ) For switches with four or more jumpers, 
you will need wipers, for otherwise the switch is likely to work 
unreliably. 

13. Assembly of the Multiple Switches. Before any of the 
multiple switches can function, however, it must first be assem- 
bled. 

Into the base we have to insert a number of nuts and bolts to 
hold wire connections and wipers. Just where these are inserted 
depends on the "type of switch we desire to construct, two-position, 
or four -position, or some other type. 

Into the top of the switch we must insert a number of jumpers 
in order to make and break contacts. Each jumper is inserted along 
a spoke between one ring and the next. Just where the jumpers are 
inserted again depends on the type of switch we desire to construct. 

In order for the switch to stay in a position to which it is 
turned, the body of the jumper must line up with the valleys between 
the ridges on the wipers, and these valleys must be in line with the 
spoke; then the jumpers will have a tendency to catch in the valleys, 
as they should, to hold the switch in position (see Figure 25, end 
view). 

- 19 - 



Note that in some drawings of the multiple switches, the 
rings and spokes are drawn as thin lines; these lines are not ac- 
tually drawn on the switch discs nor the switch bases; nor do they 
represent electrical lines connecting terminals; instead they are 
drawn to make the arrangement clearer. 




Figure 26 — Three position switch, six decks (or poles or levels) 



Now suppose we wanted to assemble a switch which would 
have any one of three positions A, B, and C, and which would be 
capable of switching every one of six different circuits. A way in 
which that switch could be assembled is shown in Figure 26, in 
which both the top and the bottom of the switch are drawn over each 
other. Six jumpers are inserted in the top of the switch, shown as 
W///A in Figure 26. It is important that jumpers ordinarily be 
inserted in pairs opposite each other, for reasons of mechanical 
balancing, so that the top of the switch will stay parallel to the 
bottom of the switch. A total of six times six or 36 nuts and bolts 
are inserted in the bottom of the switch, in the spots marked 



-20 - 



in Figure 26. They are in groups of six called decks (also called 
poles, or levels); these decks are electrically independent, and they 
enable us to switch 6 different circuits. In the base, the bolts be- 
longing in any one deck in Ring 1 or Ring 3 are connected together 
by wire, as shown by the heavy line; they may be connected with one 
of the short wires 1-1/2 inches long. They are made electrically 
common; in other words, they are commoned. Together they con- 
stitute what is called a transfer contact . 

Let us now consider the layout of the spokes and the rings and 
the 64 holes which they produce. We can see that we can assemble 
a switch in a number of different ways. This is the advantage of 
the design of the multiple switch we have chosen (patent 2848568). 
Here are the types of switches that can be made with these parts: 





Maximum 


Number of Positions 


Number of Decks 


2 


16 


3 


10 


4 


8 


5 


6 


6 to 8 


4 


9 to 16 


2 



If nuts and bolts did not cost anything, we could insert 64 nuts 
and bolts into the base of each switch and leave them there — ready 
for use in any switch. Actually, because the kit has a limited supply, 
it may be necessary to move nuts and bolts from one switch to another 
in order to make the different machines we want. 

In the case of jumpers and wipers, we shall fairly often have to 
move them to different places, in order to make different switches 
for different machines. 

14. Additional Material . You may obtain additional or replace- 
ment material for this kit by buying it at a local store, or by writing 

to us. Obviously, if your battery runs down, or if you want more wire, 
or if you want more nuts and bolts, the easy thing to do is to buy them 
in your neighborhood. But for more switch discs or more jumpers, 
etc. , you will probably need to write us. Prices for these items are 
listed on a price list enclosed with the kit or obtainable on request. 

15. Labels. The best procedure for making labels is: (1) type 
them out or write them out neatly on paper; (2) cut them out; (3) fasten 

- 21 - 



them on the board with cellophane tape. 

16. Templates . In work with electrical circuits we need to 
lay out beforehand what we are going to do. We need to design on 
paper how we are to connect the different pieces of material. For 
this purpose, we use circuit diagrams, wiring lists, and templates. 

A circuit diagram , as mentioned before, shows the scheme of 
connection of batteries, switches, lights, etc. , in order to make the 
circuit. In a circuit diagram we pay little attention to the actual phy- 
sical location of the material; we just show a diagram of its arrange- 
ment. 

In a wiring list , we name the terminals, by words or letters or 
numbers, and we state, for every part of the circuit, what terminal 
is connected to what terminal. In a wiring list again we pay no atten- 
tion to the actual spatial locations of the terminals. For example, if 
without drawing the wire, we write "to ", we are using the prin- 
ciple of a wiring list. 

In a template , the case is different; we show the actual wiring 
and the approximate relative spatial location of the different pieces 
of material used in the circuit. In other words, we draw an accur- 
ate geographical map of where the terminals are, and then we indic- 
ate the wiring either by drawing lines for the connections or by writ- 
ing notes showing the connections. For the experiments in this man- 
ual, templates on the actual scale are included in the kit. 

In each experiment in the Brainiac kit, the important part of 
the wiring is on the rear side of the panel. Accordingly, each tem- 
plate shows a full scale picture of the rear of the panel. It is there- 
fore a mirror image: what is on the right in the drawing in the man- 
ual is on the left in the template; and vice versa. Of course, some 
of the information appearing on the template belongs on the front side 
of the board: the labels of the switches, their positions, and the 
lights; and the location of the jumpers in the discs. If one pays care- 
ful attention to the two drawings, one in the manual and one on the 
template, the way the hardware and labels actually are arranged 
should become quite clear. 

17. Trouble -Shooting. After you have wired up a machine, 
and start to play with it, you are likely to find that it does not work 
entirely correctly. All engineers worth their salt who do any kind 
of significant work with electrical circuits discover when they first 

- 22 - 



assemble a new piece of equipment that it does not work properly. 
Finding out the reasons why and removing the causes of malfunction- 
ing, the process known as trouble -shooting , therefore, is an import- 
ant and essential part of making any piece of equipment start working 
and stay working; and good trouble -shooting is the mark of a good 
engineer. 

In order to trouble -shoot, it is helpful to have a systematic 
and logical checklist of questions to be answered one after another, 
and in addition testing apparatus which will tell whether a part of a 
circuit actually does what it is supposed to do. In order to test mach- 
ines made with a Brainiac kit, the essential piece of testing apparatus 
is what is called a continuity tester . A simple form of such a tester 
is a flashlight battery, a lamp, and two wires with bare ends, conn- 
ected as shown in Figure 27 . Then, when you take the ends of the 
two wires, and touch a certain pair of terminals, if you obtain a 
light, you know that that part of the circuit is connected, is contin- 
uous; while if you obtain no light, you know that that part of the cir- 
cuit is not connected, is isolated. Then, you compare what your 
tester shows to be actual fact with what you are supposed to have 
according to the circuit diagram, and you have either verified the 
correctness of that part of the circuit, or located some trouble. 

Here are some checklist questions which make a beginning at 
trouble -shooting: 

(1) Does each wire actually make contact with each 

terminal to which it is fastened? 

(2) Does each jumper actually make contact with the 

wiper at each terminal, as its switch turns? 

(3) Does each lamp really light? 

(4) Is there electricity in the battery? 

(5) Has any wire broken inside its insulation? 

(6) Is there a mistake or typographic error in the 

diagram or the instructions? (This question 
must always be asked, because no author or 
printer is infallible. ) 

(7) Does each wire go where it should? 

(8) Has each label been fastened on in its right place? 

(9) Is each jumper in its right place ? 
(10) Is each terminal in its right place? 



23 - 




^4 



Figure 27 — Continuity Tester 

If you can locate and remove trouble skillfully, you can be well 
satisfied with what you have learned. 

18. Design for a Stand . When working on wiring and assemb- 
ling a Brainiac machine, it is convenient to make a simple stand for 
holding the panel upright, so that you can work on both sides. Here 
is a design for a stand which will do this. 

1. Take two pieces of rectangular wooden rod about 1 inch by 
1 inch by 9 inches long: 

Narrow Slot 
(^ (drawn exaggerated) 




Figure 28 



2. Saw a slot in the center of each piece of rod about 2/3 of the 
way through. 

3. With a file, widen and rub down the sides of the slot so that 
the Brainiac panel fits into the slot snugly, but not too tightly nor too 
loosely. 

4. Then for wiring, assembling, displaying, etc. , the panel, 
held in the stand, looks like: 



Figure 29 



24 - 



BRAINIACS - 



Small Electric Brain Machines 

Materials in the Kit and 
How To Assemble Them 

Edmund C. Berkeley 



Copyright ^ 1966 by Berkeley Enterprises, Inc. 



Published by Berkeley Enterprises, Inc. 
315 Washington St. , Newtonville, Mass. 02160 



First printing, January, 1966 



Introduction 

This report and the accompanying kit and literature present 
Brainiacs (*0 , small electric brain machines. Ihey are electrical 
machines which are able to calculate and reason automatically al- 
though they are too small to perform operations one after another 
automatically. They show, with the least hardware that we have yet 
been able to work out that still allows interesting experiments, the 
fascinating power and variety of computing and reasoning circuits. 
There are over 200 experiments. 

Each of the machines uses one flashlight battery, not more 
than ten flashlight lamps, and not more than six multiple switches. 
All connections are made with nuts and bolts, and no soldering is 
required; the kit is completely safe. The kit, though inexpensive 
and convenient for constructing Brainiacs, is howeve'r not necessary; 
and some persons will prefer to construct their Brainiacs using other 
materials. 

The descriptions of the experiments are contained in the book 
"Brainiacs — 201 Small Electric Brain Machines and How to Make 
Them". The first thing to do is to read carefully: 

Chapter 1 - Small Electric Brain Machines — Some 
Questions and Answers 

Chapter 2 - Circuits and Circuit Diagrams 
Then this manual should be read, since it describes the materials 
in the kit and how to assemble them. Then a simple experiment 
from the book should be selected, constructed, and tried. It would 
be sensible to choose experiment No. 1 on page 9, which is also 
shown in the first template. 

If you find that at first you have some difficulty in understand- 
ing all that is in this kit, TAKE YOUR TIME and think; make first 
the simpler machines; then try the more complicated ones. To make 
a machine that will reason and calculate you too must reason and cal- 
culate. 

We hope that you find the experiments and the kit interesting, 
entertaining and amusing, and that you will enjoy playing with the kit 
and entertaining your friends with the little machines that you make. 
Any comments, suggestions for new experiments, and corrections, 
will be gratefully received. We shall be glad to hear from you. 

Edmund C. Berkeley 

- 2 - 



MATERIALS IN THE KIT AND HOW TO ASSEMBLE THEM 

With the Brainiac Electric Brain Construction Kit anyone can 
put together the machines of the types described in the experiments 
(and many more besides), so that they will perform operations of 
reasoning and computing. 

The kit is harmless. It runs on one flashlight battery. Wires 
are connected by fastening them to the same nut and bolt and tighten- 
ing the connection by gripping them between two bolts. No heat or 
soldering iron is required. DO NOT CONNECT this kit or any part 
of it to any home or industrial electrical power outlet; you are likely 
to destroy the material, and you may hurt yourself. 

The kit is simple, but nevertheless it takes effort and work to 
put the material together to make a functioning electric brain We 
urge you to take your time. If necessary, read the instructions sev- 
eral times. If the instructions are still not clear, read ahead and 
then return. 

1. Parts List. The kinds of parts contained in the kit are the 
following: 

Insulated wire 

Battery box 

Bulbs, flashlight, 1-1/2 volts 

Socket parts for flashlight bulbs, holding five together 

Short bolts, 6/32, 1/2 inch long 

Hexagonal nuts, 6/32, 1/4 inch diameter 

Spintite blade 

Panel, masonite, rectangular, punched 

Multiple Switch Discs, masonite, circular, punched 

Long bolts, 6/32, 7/8 inch, for center pivot, etc. 

Washers, hard, cardboard 

Washers, soft, sponge rubber 

Jumpers, metal, brass 

Wipers, phosphor bronze 

In addition an ordinary size I) flashlight battery. , 1/2 volt, is needed 

Each of these items will now be described. (Note- JV-ui , - 1 to 
13 are not in this manual but in the book "Brainiac s"^nd 



studied before the Eigures in this manual are studied. ) 



sh uld be 



3 - 



2. 
sulation 



Wire. The kit provides a coil of wire covered with in- 



This is like the wire connecting a lamp to a wall plug, 
for example, but adapted for handling a much smaller amount of 
electricity. Also, instead of two wires together making two paths 
for electricity, here is one wire only. In the Brainiac wiring that >, 
you will do, the wire follows a single path running from one end of 
the battery through some kind of loop to the other end of the battery, 
thus making a complete circuit. 



Your wire needs to be cut apart with a cutting pliers into 
pieces. A convenient length for many pieces is 18 inches, but some 
pieces can be shorter, about 8 inches long. About 3/4 of an inch of 
Insulation should be removed at each end of each piece. You can 
(.rim this off neatly with a dull knife. Also, a small amount of wire 
should be stripped of insulation and cut into pieces about 2 inches, 
long. Ihese pieces of bare wire make transfer contacts, as will 
be explained later. 

3. Battery . An ordinary flashlight battery, size D, provides 
about 1 and 1/2 volts. A volt is a unit of electric pressure or 
electric potential. A battery acts like a pump, and pumps electric- 
ity from one end of the battery around a circuit to the other end of 
the battery. A flow of electricity is an electric current . The fila- 
ment of a bulb through which the electricity flows provides a 
narrowness or a restriction or a resistance to the flow, so that it 
heats up and glows with "friction" as electricity flows through it. 

4. Battery Box . The battery box consists of a scored, glued 
piece of cardboard which will readily fold into a box of the right 
size to hold the battery. At each end of the box is a small hole. 
Through this hole from the inside of the box insert a bolt (on which 
a washer has been threaded, see Figure 15); then fasten the bolt 

Bare wire , washer ,Washer 

Insulated 



wire 
1 




ft 

3olt f f 

2 Nuts' 






Battery in Box 



Bare wire 

r 




_olt f 
\ A Insulated 
Nuts w ire 



Box 



figure 15 
- 4 - 



with a nut on the outside of the box. Ihe battery terminal connect- 
ion is fastened to the projecting bolt with a second nut. Ihe box 
will now hold a battery snugly, giving good contact. The battery 
box may be tied securely to the panel with a tight string around it 
and passing through holes in the panel. 

5. Bulbs. You have small flashlight bulbs in the kit. Ihey 
will glow from a single flashlight battery. In order to make them 
light, you have to run one wire from the bottom metal plate of the 
battery to the side of the bulb, and another wire from the top of the 
flashlight battery to the center of the base of the bulb. Your conn- 
ections must be clean, not oily, nor corroded. Examine your 
bulbs closely from time to time to make sure that the filament, the 
little slender wire that you see inside the glass bulb, is all in one 
piece. If it is broken, the bulb is spoiled. 

6. Socket Parts. You have two "socket parts" for flashlight 
lamps. Each holds five lamps, in such a way that they can be 
screwed in and out of their socket holes. Views of the top, side 
and end of the socket part are shown in Figure 16. 



Top 
View 



Side 
View 



° B O c O c O c OcO ? 







End 
View 



Figure 16 — Views of Socket Part 

In order to make use of this part actually assembled in a 
machine (see Figure 17), first, short bolts (for electrical connec- 
tions to the individual bulbs) are placed in the panel an inch apart 
and fastened tightly with nuts (see A in Figure 17). 

Second, long bolts for fastening the socket part to the panel 
are passed (1) through the two small holes at the two ends (see B 
in both figures) of the socket part, and (2) through the panel, and 
fastened tightly with nuts. Third, the bulbs are screwed through 
the large holes in the top of the socket part (see C in Figure 16), 
and screwed down far enough to make tight, snug contact with the 

- 5 - 



bolt under the bulb. Since the socket part is metal, one wire con- 
nector attached to the end bolt connects all the bulbs together to one 
side of the battery (see D in Figure 17). Then the screw at the base 
of each bulb enables it to be connected to its separate source of il- 
lumination from the circuit (see E in Figure 17). 



B 



*=* *=* Q (side view, but side 

Y-'A is cut away) 




^a ^a ^a1U* d 



connector to 
second , # J ^ x ~tF one side of 

nut battery 

Figure 17 — Assembled Socket Part 



7. Nuts and Bolts . For fastenings, connections, and termin- 
als, here and there all over the machine, you have a supply of bolts 
and a supply of nuts. The nuts and bolts are of rust-proofed 
steel, and give good electrical connections. A bolt is inserted 
through any hole; then a nut is screwed down tight on the bolt holding 
it in position; then the connecting wire is wound around the end of 
the bolt coming through; then a second nut is screwed down tight on 
the wire and the bolt so as to give a tight electrical contact. 

8. Spintite Blade . In order to fasten your nuts and bolts easily, 
you will need a small screwdriver, which will fit in the slot of the bolt 
and enable it to be turned. You also have in the kit a small piece of 
hexagonal tubing (a spintite blade ) which fits over and grips the hexa- 
gonal bolt and enables it to be spun quickly down the shaft of the bolt, 
and tightened, with the screwdriver holding the bolt. 

9. Panel. In order to assemble your materials together into 
a machine, you have a rectangular panel consisting of masonite (thin 
pressed fiberboard). It contains holes for nuts and bolts so that the 
various parts of the set may be mounted together and assembled 
firmly. 

If you examine the panel, you will see two patterns of holes. 
One pattern (see Figure 18) consists of 102 holes arranged in sev- 
eral rows through the middle of the panel from end to end. 



6 - 



Figure 18 

In this set of holes, all the hardware of a Brainiac machine is 
mounted except the "multiple switches", which will be explained 
in a moment. The second pattern consists of four rosettes of 65 
holes in a circular arrangement (see Figure 19). These are the 
"bases" of the multiple switches. 




Pointer 
arrowhead 
Spoke 2 showing 
position j 
of disc/ 
Spoke 1 



Spoke 



Figure 19 — Pattern of holes in the multiple switch 

(either the "base" in the panel or the "top", 
which is the disc). Also, the system of 
naming the holes. 



10. Multiple Switches. The remaining material provided in 
the kit consists of round pieces of masonite, each containing 65 holes 



in the same circular arrangement (see Figure 19), and the hardware 
for assembling them into multiple switches, switches which are able 
to switch many circuits at the same time. Each of the circular 
pieces of masonite is about 4-3/8 inches in diameter, is illustrated 
in Figure 19, and is called a multiple switch top , or switch disc, 
or switch dial , or simply a disc . These multiple switches have 
been patented (2848568). 

In the panel each of the exactly similar sets of 65 holes is 
called a multiple switch base. In an early stage of design, the 
switch bases were separate pieces of masonite; but then it became 
evident that mounting of the hardware to make a machine would be 
better accomplished by having all the switch bases solidly connec- 
ted together in the panel. 

The top of a switch is fastened to the base of a switch by means 
of a center pivot , consisting of a long bolt, some hard washers, a 
sponge rubber washer, and a nut; the assembly of the center pivot 
is shown in Figure 20. 




Pivot bolt (long bolt), head 

Switch top 

Some hard washers 

Switch base, or panel 

Sponge rubber washer 

Another hard washer 
Nut 

Pivot bolt, shaft 



Figure 20 — Center Pivot Assembly 



Instead of individual sponge rubber washers, the kit contains 
a small piece of sheet sponge rubber out of which the individual 
washers may be cut with a scissors. Cut out each rubber washer 
to be about the same size as one of the steel washers. Cut or poke 
a small hole in the middle of washer to allow a bolt to go through it. 
It is then ready for use; it functions as a compression spring. 



The holes (except the center hole) in each switch base and 



switch top are arranged in 4 rings and 16 spokes. The rings are 
called Ring 1, 2, 3, 4 going outward, and the spokes are called 
Spoke 0, 1, 2, 3, and so on around, to Spoke 15. The counting 
starts with the spoke directly to the right, and goes counterclock- 
wise. See Figure 19. 

Each of the holes in the switch base may or may not contain 
a short bolt, called a terminal, for making connections. The con- 
nections are made using two nuts, one for fastening the bolt sec- 
urely to the switch base, and the second for holding and tightening 
a wire around the bolt so as to make a good electrical connection 
with the bolt (see Figure 21). 



Terminal bolt (short bolt K " Wiper ' bent> ridg6S UP 



■ Switch base 
First small nut- 




^*~Bare wire, looped 
-J ^ > tightly around 



Connector — -T ^-Second nut 



Figure 21 — Assembly of Wiper, Terminal Bolt, and 
a Wire Connector 



11. Jumpers. Each pair of holes in a switch top, from Ring 
1 to Ring 2 or from Ring 3 to Ring 4 (or very rarely from Ring 2 to 
Ring 3) may or may not contain a jumper , a small piece of brass 
plated metal with two prongs, as shown in Figure 22. The two 
prongs fit into holes in the switch disc and are pressed down, like 
a clasp or T fastener, as shown in Figure 23. A jumper serves to 
make and break electrical contact as the switch is turned. 



■ Jumper prongs 




■ Jumper body - 
Side view End view 

Figure 22 — Jumper, not mounted 



-Jumper prongs bent down 



Switch top 



Jumper body 



-^=7 



Side view End view 

Figure 23 — Jumper, inserted in two adjacent holes along a spoke 

12. Wipers . In between the jumper and the bolt, in the assem- 
* bled multiple switch, is inserted a wiper, a springy piece of phosphor 
bronze with a hole and two small ridges. The shape of the wiper un- 
bent, as it comes in the small envelope, is shown in Figure 24. The 
purpose of the wiper is to improve the electrical contact between, the 
top of the switch (the disc containing the jumpers) and the bottom of 
the switch (the panel containing the bolts and nuts for the terminals). 
These wipers have been patented (2848568). 



Hole 



& 




Wiper, ridges down 
Top view End view 

Figure 24 — Unbent wiper 



Ridges of 
wiper 



_^I v^. 



wiper 
bent 



^< JVw i 



— disc ■ 
.jumper. 



wiper bent 



•E 



s-*. 



> y^< J 

wiper /* . ^tL>: 
bent^ — 



Valley 
of wiper 



■ panel ■ 



► £_i 



-bolt 



Side view End view 

Figure 25 — Assembly of wipers 



10 - 



The way in which the wiper is assembled is shown in Figure 
25, and is as follows: (1) thread the bolt through the wiper, with 
its ridges down; (2) fasten the bolt not too tightly to the panel; 
(3) align the wiper with the spoke (or radius) of the switch; (4) now 
fasten the bolt tightly; (5) bend the wiper gently upwards and over 
the bolt, with the ridges up, in such a way that the wiper will slide 
neatly on the jumper, resting in its valley between the ridges; 
(6) assemble the multiple switch with (probably three) washers in 
between the disc and the panel; (7) adjust the amount of bending the 
wipers so that they push up and down nicely against the jumpers as 
the switch turns. 

For multiple switches with only two jumpers evenly spaced, 
or only three jumpers almost evenly spaced, you will not need wip- 
ers and should not use them, for such switches will work entirely 
properly without wipers. In these cases, you will need to make 
sure that the slots in the heads of the bolts are lined up with the 
spoke, so that the jumpers themselves will position (or detent ) 
along the spoke right above the bolts. (In assembling a switch with- 
out wipers, you need only one or two spacing washers along the 
center bolt, not three. ) For switches with four or more jumpers, 
you will need wipers, for otherwise the switch is likely to work 
unreliably. 

13. Assembly of the Multiple Switches . Before any of the 
multiple switches can function, however, it must first be assem- 
bled. 

Into the base we have to insert a number of nuts and bolts to 
hold wire connections and wipers. Just where these are inserted 
depends on the type of switch we desire to construct, two-position , 
or four -position, or some other type. 

Into the top of the switch we must insert a number of jumpers 
in order to make and break contacts. Each jumper is inserted along 
a spoke between one ring and the next. Just where the jumpers are 
inserted again depends on the type of switch we desire to construct. 

In order for the switch to stay in a position to which it is 
turned, the body of the jumper must line up with the valleys between 
the ridges on the wipers, and these valleys must be in line with the 
spoke; then the jumpers will have a tendency to catch in the valleys, 
as they should, to hold the switch in position (see Figure 25, end 
view). 

- 11 - 



Note that in some drawings of the multiple switches, the 
rings and spokes are drawn as thin lines; these lines are not ac- 
tually drawn on the switch discs nor the switch bases; nor do they 
represent electrical lines connecting terminals; instead they are 
drawn to make the arrangement clearer. 




Figure 26 — Three position switch, six decks (or poles or levels) 



Now suppose we wanted to assemble a switch which would 
have any one of three positions A, B, and C, and which would be 
capable of switching every one of six different circuits. A way in 
which that switch could be assembled is shown in Figure 26, in 
which both the top and the bottom of the switch are drawn over each 
other. Six jumpers are inserted in the top of the switch, shown as 
W///A in Figure 26. It is important that jumpers ordinarily be 
inserted in pairs opposite each other, for reasons of mechanical 
balancing, so that the top of the switch will stay parallel to the 
bottom of the switch. A total of six times six or 36 nuts and bolts 
are inserted in the bottom of the switch, in the spots marked # 



12 



in Figure 26. They are in groups of six called decks (also called 
poles, or levels); these decks are electrically independent, and they 
enable us to switch 6 different circuits. In the base, the bolts be- 
longing in any one deck in Ring 1 or Ring 3 are connected together 
by wire, as shown by the heavy line; they may be connected with one 
of the short wires 1-1/2 inches long. They are made electrically 
common; in other words, they are commoned . Together they con- 
stitute what is called a transfer contact . 

Let us now consider the layout of the spokes and the rings and 
the 64 holes which they produce. We can see that we can assemble 
a switch in a number of different ways. This is the advantage of 
the design of the multiple switch we have chosen (patent 2848568). 
Here are the types of switches that can be made with these parts: 





Maximum 


Number of Positions 


Number of Decks 


2 


16 


3 


10 


4 


8 


5 


6 


6 to 8 


4 


9 to 16 


2 



If nuts and bolts did not cost anything, we could insert 64 nuts 
and bolts into the base of each switch and leave them there — ready 
for use in any switch. Actually, because the kit has a limited supply, 
it may be necessary to move nuts and bolts from one switch to another 
in order to make the different machines we want. 

In the case of jumpers and wipers, we shall fairly often have to 
move them to different places, in order to make different switches 
for different machines. 

14. Additional Material . You may obtain additional or replace- 
ment material for this kit by buying it at a local store, or by writing 

to us. Obviously, if your battery runs down, or if you want more wire, 
or if you want more nuts and bolts, the easy thing to do is to buy them 
in your neighborhood. But for more switch discs or more jumpers, 
etc. , you will probably need to write us. Prices for these items are 
listed on a price list enclosed with the kit or obtainable on request. 

15. Labels. The best procedure for making labels is: (1) type 
them out or write them out neatly on paper; (2) cut them out; (3) fasten 

- 13 - 



them on the board with cellophane tape. 

16. Templates . In work with electrical circuits we need to 
lay out beforehand what we are going to do. We need to design on 
paper how we are to connect the different pieces of material. For- 
tius purpose, we use circuit diagrams, wiring lists, and templates. 

A circuit diagram , as mentioned before, shows the scheme of 
connection of batteries, switches, lights, etc. , in order to make the 
circuit. In a circuit diagram we pay little attention to the actual phy- 
sical location of the material; we just show a diagram of its arrange- 
ment. 

In a wiring list , we name the terminals, by words or letters or 
numbers, and we state, for every part of the circuit, what terminal 
is connected to what terminal. In a wiring list again we pay no atten- 
tion to the actual spatial locations of the terminals. For example, if 
without drawing the wire, we write "to. . . M , we are using the prin- 
ciple of a wiring list. 

In a template , the case is different; we show the actual wiring 
and the approximate relative spatial location of the different pieces 
of material used in the circuit. In other words, we draw an accur- 
ate geographical map of where the terminals are, and then we indic- 
ate the wiring either by drawing lines for the connections or by writ- 
ing notes showing the connections. For some illustrative Brainiac 
experiments, templates on a reduced scale are included in the kit. 

In each experiment in the Brainiac kit, the important part of 
the wiring is on the rear side of the panel. Accordingly, each tem- 
plate shows ascaled picture of the rear of the panel. It is there- 
fore a mirror image: what is on the right in the drawing in the man- 
ual is on the left in the template; and vice versa. Of course, some 
of the information appearing on the template belongs on the front side 
of the board: the labels of the switches, their positions, and the 
lights; and the location of the jumpers in the discs. If one pays care- 
ful attention to the two drawings, one in the manual and one in the 
template, the way the hardware and labels actually are arranged 
should become quite clear. 

17. Trouble-Shooting. After you have wired up a machine, 
and start to play with it, you are likely to find that it does not work 
entirely correctly. All engineers worth their salt who do any kind 
of significant work with electrical circuits discover when they first 

- 14 - 



assemble a new piece of equipment that it does not work properly. 
Finding out the reasons why and removing the causes of malfunction- 
ing, the process known as trouble -shooting , therefore, is an import- 
ant and essential part of making any piece of equipment start working 
and stay working; and good trouble -shooting is the mark of a good 
engineer. 

In order to trouble-shoot, it is helpful to have a systematic 
and logical checklist of questions to be answered one after another, 
and in addition testing apparatus which will tell whether a part of a 
circuit actually does what it is supposed to do. In order to test mach- 
ines made with a Brainiac kit, the essential piece of testing apparatus 
is what is called a continuity tester . A simple form of such a tester 
is a flashlight battery, a lamp, and two wires with bare ends, conn- 
ected as shown in Figure 27. Then, when you take the ends of the 
two wires, and touch a certain pair of terminals, if you obtain a 
light, you know that that part of the circuit is connected, is contin- 
uous; while if you obtain no light, you know that that part of the cir- 
cuit is not connected, is isolated. Then, you compare what your 
tester shows to be actual fact with what you are supposed to have 
according to the circuit diagram, and you have either verified the 
correctness of that part of the circuit, or located some trouble. 

Here are some checklist questions which make a beginning at 
trouble -shooting: 

(1) Does each wire actually make contact with each 

terminal to which it is fastened? 

(2) Does each jumper actually make contact with the 

wiper at each terminal, as its switch turns? 

(3) Does each lamp really light? 

(4) Is there electricity in the battery? 

(5) Has any wire broken inside its insulation? 

(6) Is there a mistake or typographic error in the 

diagram or the instructions? (This question 
must always be asked, because no author or 
printer is infallible. ) 

(7) Does each wire go where it should? 

(8) Has each label been fastened on in its right place? 

(9) Is each jumper in its right place? 
(10) Is each terminal in its right place? 



-15 




H I 



Figure 27 — Continuity Tester 



If you can locate and remove trouble skillfully, you can be well 
satisfied with what you have learned. 

18. Design for a Stand . When working on wiring and assemb- 
ling a Brainiac machine, it is convenient to make a simple stand for 
holding the panel upright, so that you can work on both sides. Here 
is a design for a stand which will do this. 

1. Take two pieces of rectangular wooden rod about 1 inch by 
1 inch by 9 inches long: 

Narrow Slot 
^7 (drawn exaggerated) 




Figure 28 



2. Saw a slot in the center of each piece of rod about 2/3 of the 
way through. 

3. With a file, widen and rub down the sides of the slot so that 
the Brainiac panel fits into the slot snugly, but not too tightly nor too 
loosely. 

4. Then for wiring, assembling, displaying, etc. , the panel, 
held in the stand, looks like: 



Figure 29 



- 16 



First Booklet 

HOW TO ASSEMBLE 

® 
BRAINIACS 

Containing 

Part 1 : Brainiac Kit Parts and Their Use 

Part 2: NINE Electrical Research Experiments 



by 

Dorothy D. Zinck 



Copyright 1959 by Berkeley Enterprises, Inc. 

Sold by Cardinal Wood Products 

9229 East Prairie Road 

Skokie, 111. 

Published by Berkeley Enterprises, Inc. 
815 Washington St. 
Newtonville 60, Mass. 

First printing, August, 1959 



Introduction 



Booklet 1 contains two parts. Part 1 describes the Brainiac kit 
parts and explains their use. Part 2 consists of a number of electri- 
cal research experiments which will make you familiar with your 
equipment, help you understand how it is to be assembled, and pre- 
pare you for the more advanced experiments in Booklet 2. 

If you are already familiar with the principles of electricity, you 
will be able to do all of the experiments quickly. Be sure not to skip 
any, however, since you will often use equipment assembled in one 
experiment for the next experiment. 

If you have not had much experience with electricity, you will 
need to go more slowly. As you complete each experiment, read 
the "What happened?" section several times, tracing the circuit 
through the diagram as you read. Do not go on to the next experi- 
ment until you are sure you understand not only WHAT you have 
accomplished, but also WHY the experiment worked. 

You will find that the time you devote to this booklet will be well 
spent. To attempt to complete the experiments in Booklet 2 without 
finishing the experiments in this booklet would be much like learning 
advanced algebra or trigonometry without first learning your multi- 
plication tables; or studying English literature, physics, chemistry, 
or history without first learning to read. 

If you DO understand the experiments in Booklet 1, you will have 
the background information necessary in order to assemble the com- 
puting and reasoning machines described in Booklet 2. 



Libertyville, 111. Dorothy D, Zinck, author 

August, 1959 



2 - 



Part 1 
BRAINIAC KIT PARTS AND THEIR USE 

Unpacking your kit 

Spread the contents of your Brainiac kit on the table as follows: 

1. Remove the items from the small box (but do not open the 

plastic bags). 

2. With the screwdriver pry the staples from the small box 

so you can remove it. 

3. Unscrew the two white discs (which look like wheels). You 

will find there are actually four discs. Put the discs on the 
table, and the bolts, nuts, and washers in the small box. 

4. Remove the large rectangular panel, then the two pieces of 

wood taped to the kit box. Set the panel upright in the slots 
of the two pieces of wood. 



Identifying your Brainiac kit parts 

Since you will use the same parts over and over again in your 
experiments, it is important for you to recognize each part by name 
and by appearance, and to know its use. While you have the contents 
of the Brainiac kit on the table before you, read through the list be- 
low. Find each part which is described, and examine it carefully. 
By doing this now, you will be able to understand and complete the 
experiments much more quickly than would be possible otherwise. 

A. Brainiac Panel (the large rectangular panel) . The Brainiac 
panelboard, or panel, has two main purposes: (1) It is a mounting 
board on which you assemble and fasten your equipment. (2) When 
you have completed your experiment, it is an instrument panel with 
round movable switches with which you control your machine. You 
can write notes directly on the panelboard with an ordinary lead pen- 
cil. The marks will erase easily when you are ready for a new ex- 
periment. 



- 3 - 





F. Socket Part 



A. Brainlac Panel (the large Long Bolt Short Bolt Hex Nut 

rectangular panel) ± ^ 1/2 ^ 



Top 
-^Bottom 



G. Bolts and Hex Nuts 



B. Battery 





H. Screwdriver 




L Spintite Blade 



O 




-Spoke 



White Red 

J. Switch Discs 



Wire 
Connection 



Prong v 



C. Battery Box 







• Not inserted 
•Inserted 



D. Wire Coil 

Filament 
Glass bulb 
Metal side 
Insulation 
Metal base 

E. Lamp 



K. Jumper 





L. Wiper 



-4 




M. Hard 
Washer 



N. Soft 
Washer 



B. Battery, The battery supplies the electric current for your 
experiment or machine. The end with the metal button is the top; the 
flat end, the bottom. (If you did not receive batteries with your 
Brainiac kit, you can get the right kind by obtaining a size D flash- 
light battery of 1-1/2 volts. Batteries are not packed in the kit at 
the factory because they lose their power if they are kept too long. ) 

C. Battery Box . The battery box holds the battery in place, and 
provides ways whereby wires can be connected to each end of it. Read 
the instructions on the box carefully; then fold it together. 

At each end of the box there is a small hole. Insert a bolt through 
the end of the box from the inside of the box; then fasten it with a nut 
on the outside of the box. Then the wire connection can be fastened 
with a second nut. The box should now hold a battery cell properly 
and give good contact. To fasten the battery box containing the bat- 
tery to the board, tie a loop of string or wire around the box, and 
through two holes in the board. 

Test the connections from the battery to see that the heads of th« 
bolts rest snugly and firmly against the ends of the battery. If there 
is not enough pressure from the ends of the cardboard box against 
the ends of the battery, cut out some cardboard washers, and insert 
them between the heads of the bolt and the ends of the battery box 
so as to produce firmer, more positive contact. 

D. Wire Coil. The wire coil contains 25 feet of insulated cop- 
per wire. The plastic, or insulation, around the wire will not con- 
duct electricity. The wire itself will. For your experiments you 
will cut the wire from time to time into short lengths and fasten then 
to various parts to carry electricity from one part to the next. Do 
not cut the wire now. 

E. Lamp. The lamp is a lightbulb such as used in flashlights. 
It will glow when properly connected to the battery by wires. The 
parts of the lamp are: 

1. The glass bulb, which does not conduct electricity. 

2. The filament — a fine wire inside the bulb, which glows 

as electricity passes through it. 

3. The metal side — which provides one way for electricity 

to go into or out of the lamp. 

- 5 - 



4. The metal base — which provides the second way for el- 

ectricity to go into or out of the lamp. 

5. The insulation between the metal side and the metal base 

which prevents them from connecting electrically with 
each other. 

F. Socket Part. The socket part holds the lamps upright. Each 
socket part has seven holes — a small one at each end to bolt the part 
to your Brainiac panelboard, and five larger ones for holding lamps. 

Each of the larger holes has a bent notch which grips the lamp 
as you screw it in or out. 

G. Bolts and Hex Nuts. Bolts and hexagonal nuts (or hex nuts) 
are used as "terminals ,r for fastening wires. They are also used to 
attach your equipment to the Brainiac panelboard. The long bolts 
are 1 inch long; the short ones, 1/2 inch long. The screw thread 
specification is 6/32. 

H. Screwdriver . The Brainiac screwdriver is long and slender 
so it will not get in the way when you work. It has a clip so you can 
keep it handily in your pocket. 

I. Spintite Blade . The spintite blade works something like a 
screwdriver except the hollow end fits over the hex nut. You hold 
the bolt steady with the screwdriver, place the spintite blade over 
the hex nut, then twirl the spintite blade with your fingers so it 
spins the hex nut onto the bolt. It can also remove a nut from the 
bolt. 

J. Switch Discs. The patented switch discs (the four "wheels" 
you unscrewed from the Brainiac panelboard) enable you to control 
your experiment. As you turn a disc it makes or breaks the electri- 
cal contact so that the current is transferred from one set of wires 
to another, or is turned on or off. (Patent No. 2848568) 

The discs are all alike. One side is white, the other red. Each 
has 64 holes set in a pattern which resembles 16 spokes of a wheel, 
with a 65th hole in the center. These match the holes in the black 
rectangles on the Brainiac panelboard. 

K. Jumper . The jumper is a small piece of brass plated metal 
with two prongs. It makes and breaks the electrical contact as you 

- 6 - 



turn the switch disc. If the jumper on the disc touches two wired ter- 
minals on the panelboard beneath it, it conducts electricity from one 
to the other. 

The jumper is fastened to a switch disc by inserting the two prongs 
into two holes along a spoke of the disc, and then pressing the ends to- 
wards each other and down. 

L. Wiper . The wiper, a patented Brainiac part made of phosphor 
bronze, improves the electrical connection between the jumper in the 
switch disc and the terminal on the Brainiac panelboard. Wipers are 
needed only when your switch has four or more jumpers. (Patent 
No. 2848568) 

M. Hard Washer. The hard fiber washer is used for spacing 
and for holding. 

N. Soft Washer . The soft washer is used to put a "spring" into 
a switch. It is thick and made of sponge rubber. 

In addition to the above parts you will need a dull knife, such as a 
paring knife, and adhesive tape (bandaids will do). 



To get fresh new flashlight batteries or additional bolts, hex 
nuts, or other parts, try your local hardware store. If they 
do not have what you need, write to: 

BRAINIAC 

Cardinal Wood Products 
9229 East Prairie Road 
Skokie, 111. 



WARNING! DO NOT attach any parts of your Brainiac equipment to 
any electrical outlets in your house or elsewhere. They are not made 
for that purpose. . . . only for use with a flashlight battery. You may 
ruin your equipment and hurt yourself if you use any other source of 
power. 



7 - 



Part 2 
ELECTRICAL RESEARCH EXPERIMENTS 



The electrical research experiments in this booklet have been 
designed for two reasons. First, if you do one experiment at a time, 
in the proper order, you will understand how electricity works. When 
you have completed all these experiments , you will be ready to work 
out the problems requiring more thought in Booklet 2, and eventually 
you will be able to design your own machines. Second, although you 
are learning while you assemble the parts, the experiments are fun 
because they DO something when you complete them correctly. 

How to Begin 

First open the plastic bags of small parts by carefully removing 
the staples. Keep all parts in their bags except when you use them. 
Then they won f t roll on the floor and get lost, and it will be easy to 
find what you need. When you are ready to begin an experiment, 
select the parts needed for that experiment and lay them on the table. 
If you are not certain what part is meant, look up the code letter 
(which is shown in ( ) after the part name) under KIT PARTS AND 
THEIR USE. Keep each experiment assembled until you have checked 
to see whether it is needed for the next experiment. 



Experiment No. 1. LIGHTING A LAMP 

You will need: 1 battery (B) wire coil (D) 1 lamp (E) 
adhesive tape a dull knife 

What to do : 

1. Cut two 8 -inch long pieces of wire from the coil. At each 
end, 3/4 inch from the top, run your knife around the 
wire so it cuts through the plastic insulation. Scrape 
the insulation off the ends of the wires so they look like 
this: 



k^>^ *^~ insulated ^_bare 

2. Wind the bare end of one of the wires around the side of 
the lamp. 



- 8 



3. Fasten the other bare end to the base (flat part) of the 

battery with adhesive tape. 

4. Fasten one end of the second wire to the top of the battery 



with adhesive tape, 
like this: 




Lamp 



Your equipment should now look 
Circuit 

Lamp* 



— Battery 



v 

Adhesive 

5. Touch the metal button at the base of the lamp with the 
loose end of the second wire. If your experiment is 
successful the lamp will light. If not, read Experiment 
No. 2, then find and correct the cause of the failure. 

What happened ? You made a complete electrical circuit from 
your battery to the lamp and back. The battery is like a pump. It 
builds up a supply of electrons (flowing particles, or tiny drops, of 
electricity) at the top, and a lack of electrons at the bottom. The 
electrons flow from the top of the battery through the first wire, 
into the lamp from the side, through the filament, out the base of 
the lamp, and back to the battery. They are then "pumped" to the 
top of the battery, and the circulating flow begins again. 

As electrons rush through the filament in the lamp, which is 
very narrow, the friction of their passing heats the filament until it 
becomes white-hot, giving light. 



Experiment No. 2. TROUBLE -SHOOTING 

When a circuit that should work does not work, you have to find 
and correct the trouble. This is called trouble -shooting. Here are 
the points to check or verify in your first experiment (or any other 
experiment) which does not work: 

1. Contacts. Do your wires all actually touch the metal parts 
to which they are attached? If there is an air space between the 
wire and the metal part, electrons cannot flow through it. Or if 
there is a bit of material such as insulation from the wire, dirt, or 
adhesive tape, between the wire and the metal, it will form an insula- 
tion that stops the electrons. Scrape the wire ends and metal parts 
with your knife to clean them. 



9 - 



2. Lamp . The filament or some other important part of the 
lamp may be broken. Try a new lamp. 

3. Battery. Your battery may be "dead", that is, it no longer 
pumps electrons. Try a new battery. 

4. Wire. Your wire may have a break in it somewhere inside 
the insulation where you cannot see it. Try another wire. 



Experiment No. 3 . INSTALLING A LAMP SOCKET PART 

You will need: Your assembled Experiment No. 1 

Brainiac panelboard (A) 1 socket part (F) 
2 long bolts, 1 short bolt, 5 hex nuts 

What to do : 

1. Insert a short bolt into the center hole of one of the 11- 

hole series in the center section of your Brainiac panel- 
board. From the back of the panelboard, tighten a hex 
nut over ihe bolt. 

2. Place the socket part over the 11 holes, with the hollow 

part next to the panelboard. Pass a long bolt through the 
the Brainiac panelboard. Tighten a hex nut over each 
bolt. 

3. Attach the bare end of an 8 inch piece of wire to the top 

of your battery with adhesive tape. 

4. Attach the bare end of another 8 inch piece of wire to the 

bottom of your battery with adhesive tape. 

5. Wind the other end of the top -of -the -battery wire around 

the end of a long bolt (see Step 2). Add a hex nut so the 
wire is held by the two nuts. 

6. Wind the end of the bottom -of -the -battery wire around 

the end of the short center bolt. Add another hex nut 
to hold it in place. 

7 . Screw the lamp into the center hole of the socket part so 

that it touches the top of the short bolt. The lamp will 

- 10 - 



light if your experiment is successful, 
light, trouble-shoot. 



If it does not 




What happened? Electrons flowed from the top of the battery (1), 
through the wire to the base of the terminal (2) you made from the 
long bolt and hex nuts, up the bolt, across through the metal socket 
part and into the side of the lamp (3), through the filament, out the 
base of the lamp through the second terminal (4) made from the short 
bolt and nuts, and back through the second wire to the battery, thus 
making a complete loop, or circuit. ( Note: Although the current 
flowed through the metal socket part from the long bolt to the side 
of the lamp, it did not flow from the base of the lamp back to the 
long bolt because the panelboard is made of material which does 
not conduct electricity. ) 



Experiment No. 4. INSTALLING THE BATTERY BOX 

You will need : Your assembled Experiment No. 3 

Battery Box (C) folded and equipped with bolts 

and nuts at each end 
2 short bolts and 3 hex nuts 
a piece of string 

What to do: 



1. Remove the adhesive tape and wires from the battery, 

and place the battery in the battery box. It does not 
matter which way the top and bottom go. 

2. Fasten the battery box snugly to the panelboard with the 

piece of string. 

3. Wrap the bare end of one wire around one of the battery 

box end bolts (terminals) and hold it in place with a hex 
nut. 



11 - 



4. Wrap the bare end of the other wire around the other 

battery box end bolt, and hold it in place with a hex nut. 

5. If your experiment is a success, the lamp will light. If 

it doesn't light — time to trouble -shoot! 

What happened ? Current flowed from the battery through the 
battery box end bolt, through the wiring, socket part, and lamp, 
through the short bolt at the base of the lamp, and through the wire 
back to the other battery box end bolt. 



Experiment No. 5. CONSTRUCTING A SIMPLE MOVING WIRE 
SWITCH 

You will need: Your assembled Experiment No. 4 

1 short bolt 1 hex nut 1 more lamp 



Second 
Lamp 




z Socket Part 



Panel 



A "Simple Moving 
Wire Switch" 



What to do : 

1. Unfasten the socket part. (See diagram) 

2. In the Brainiac panelboard insert the short bolt two holes 

from the center short bolt, so that you have a bolt, a 
hole, and your second bolt. (See diagram) 

3. Attach a hex nut to the bolt, and replace the lamp socket 

to its original position. 



- 12 



4. Insert a second lamp in the socket, directly over your 

newly inserted bolt, so the base of the lamp touches the 
bolt. 

5. Remove the wire attached at the back of the panelboard 

to the bolt at the bottom of the socket of the first lamp. 

6. If you have not been working with your panelboard in an 

upright position, now set it upright in the slots of the 
two wooden supports. 

7 . With the loose wire touch first the bolt behind one of the 

lamps, then the bolt behind the other. If your experi- 
ment is successful, each lamp will light in turn. If they 
do not, you should trouble -shoot until you find and re- 
move the cause. 

What happened ? When you removed the wire, you broke the cir- 
cuit and electrons no longer flowed through the lamp. When you 
touched the wire to the other bolt you completed a circuit to that 
lamp. The metal socket part conducts ^electricity between the long 
terminal bolt and the side of either lamp. The short bolt which 
touches the lamp conducts current between the base of the lamp and 
the wire with which you touch the bolt. 



Now before we go ahead with the next experiment, let us talk a 
little about switches in general, and the switches that you have in the 
Brainiac kit. An ordinary switch — on a railroad track for example 
— consists of some rails which can be swung one way or another way 
so as to route a train either in one direction or another direction. 
The swinging wire in the previous experiment routes electricity in 
one way or another way. 

In the Brainiac kit our switches are put together from the discs, 
the panel, and hardware, so that we can route electricity in differ- 
ent directions. How do we do this? Let us look at the discs and the 
panel. 

Each disc contains 65 holes, one in the center and the rest in 4 
circular rings of 16 holes each, lined up in 16 spokes . This disc is 
a multiple switch top. 



13 



In the panel each of the exactly similar sets of 65 holes is called 
a multiple switch base. 

The rings are called Ring 1, 2, 3, 4 going outward, and the 
spokes are called Spoke 0, 1, 2, 3 and so on around, to Spoke 15. 
The counting starts with the spoke directly to the right, and goes 
counterclockwise. See Figure 1. 



Pointer 
° \ arrowhead 

6 o X \ Spoke 2 showing 

o ° ° ^ \ position/ 

« ° « \ of disc/ 

o o o \ 

7 / ° o ° o o \Spoke 1 

o ° 

/ ° o Central « ° 

/ Pivot Hole 



O o o o o\ Spoke 

Ring: 12 3 4^ 



o o o o 

Ring: 12 3 4, 



9 \ 

\ 
\ 



/ 
15 



j ° ° 

10\ o 14 

X © O y 

11 • _ 13 

12 

Figure 1 — Showing the pattern of the holes in the multiple 
switch (either the "base" in the panel or the 
"top", which is the disc); showing also the 
system of naming the holes. 



To put together a switch, the top is fastened to the base of a 
switch by means of a center pivot, consisting of a long bolt, a sponge 
rubber washer, a second hard washer, and a nut. The assembly of 
the center pivot is shown in Figure 2. 

Each of the holes in the switch base may or may not contain a 
short bolt, called a terminal , for making connections. The connec- 



- 14 






Pivot bolt (long bolt), head 



f, MM^ifr i w si. 



• Switch top 

- One hard washer 

- Switch base, or panel 



I 



■ Sponge rubber washer 
< — Second hard washer 



-Nut 
«-Pivot bolt, shaft 



Figure 2 — Center Pivot Assembly 



tions are made using two nuts, one for fastening the bolt securely to 
the switch base, and the second for holding and tightening a wire 
around the bolt so as to make a good electrical connection with the 
bolt. 

Each pair of holes in a switch top, from Ring 1 to Ring 2 or from 
Ring 3 to Ring 4 (or very rarely from Ring 2 to Ring 3) may or may 
not contain a jumper , a small piece of brass plated metal with two 
prongs, as shown in Figure 3. The two prongs fit into holes in the 
switch disc and are pressed down, like a clasp or T fastener, as 
shown in Figure 4. A jumper serves to make and break electrical 
contact as the switch is turned. 

- Jumper prongs ■ 
Jumper body . 
Side view End view 

Figure 3 — Jumper, not mounted 




Jumper prongs bent down^ 



Switch top 



Jumper body 



Side view End view 

Figure 4 — Jumper, inserted in two adjacent holes along a spoke 

- 15 - 



We are now ready to go ahead with the next experiment. 



Experiment No. 6. INSTALLING A SWITCH DISC 

You will need: Your Experiment No. 5 
a switch disc (J) 
a jumper (K) 

4 short bolts 
1 long bolt 

5 hex nuts 

1 hard washer 

1 soft rubber washer 

an 8 -inch-long piece of wire with insulation 

scraped off 3/4 inch at each end 
a 12 -inch-long piece of wire with insulation 

scraped off 3/4 inch at one end and 1-1/2 inch 

at the other end 

What to do: 



1. In one of the rosettes of the Brainiac panelboard insert 
4 short bolts on spokes and 1 and rings 3 and 4, as 
shown by A B C and D in the illustration. Attach hex 
nuts from underneath the panel. Check the slots in the 
bolts; if they do not point toward the center hole, turn 
the bolts so they will. 




Part of a "rosette" of 65 holes 
in the Brainiac panelboard 



- 16 



2. Pick up the switch disc and the jumper. From the red 

side of the switch disc insert the prongs of the jumper 
in the two outer holes of the spoke on which the arrow 
points. Turn the disc over and bend the prongs of the 
jumper together. 

3. Remove the loose wire from the battery clamp. In its 

place, put the 12 inch wire, attaching the end on which 
3/4 inch is bare. 

4. Wind the other bare end of the 12 inch wire once around 

bolt A , making the loop as near the insulation on the 
wire as possible. Bring the rest of the bare end of the 
12 inch wire to bolt B, and attach. Place hex nuts on 
bolts A and B to hold the wires in place. 

5. Attach a bare end of the 8 -inch-piece of wire you removed 

from the battery clamp to one of the short bolts underneath 
a lamp, using another hex nut to hold it in place. Bring 
the other end of the wire to bolt D, wind it around the bolt, 
and attach a hex nut. 

6. Attach a bare end of the remaining 8 -inch wire to the short 

bolt beneath the other lamp, adding a hex nut to hold it in 
place. Bring the other end to bolt C, attach it, and add a 
hex nut to hold it in place. This completes the wiring of 
your Brainiac panelboard. 

7. Take a long bolt and hold it head down. Place a switch 

disc, white side down, on the bolt. 

8. Insert the bolt in the center hole of the disc, and add a 

hard washer. 

9. Insert the bolt with the disc into hole E in the panelboard, 

add a soft rubber washer, a hard washer, and a hex nut. 

10. Turn the switch disc so that the jumper is over B and D. 
It should light one lamp. Turn the switch disc so that the 
jumper is over A and C. It should light the other lamp. 
If it doesn't — time to trouble -shoot! 

What happened? By moving the switch disc you brought the jump- 
er in the disc in contact with either points A and C, or points B and 

- 17 - 



D. The jumper, being metal, carried electrons between the two 
points, completing the circuit for the lamp attached to that set of 
wires, and causing the lamp to light. 

Instead of having a loose and mechanically unsatisfactory switch 
(the swinging wire), we now have a firm and mechanically sound 
switch. 



Experiment No. 7. 



INSTALLING A SWITCH DISC TO SWITCH ANY 
ONE OF THREE LIGHTS 



You will need : Your Experiment No. 6; and additional hardware, 
which, as you will see, is needed from looking closely at Figure 

5, because you will be using terminals F and G to light a third 

lamp screwed into the socket part. 



The terminals A to F are in the switch base 

center pivot / Three positions or settings for the switch; 
hole / | f222 = jumper, which is in the switch disc; 

, pointer on the switch disc 
No. 1 No. 2 No. 3 

^<-3 Lamps 

- Socket 
part 




Wire 



Switch 



four wires 
Figure 5 



Results: After you have this all put together, when the pointer 
is at position 1, lamp 1 will light. When the pointer is at position 2, 
lamp 2 will light. When the pointer is at position 3, lamp 3 will 
light. Only one lamp will light at any one time. If this does not hap- 
pen, — time to trouble -shoot! 

What happened? Electricity flows along a path, from one end of 
the battery to the common terminal B A F, and then separates and 
flows along any one of three paths out of D, C, or G through the re- 



- 18 



speetive lamp 1, 2, or 3, and then back along a common path to the 
other side of the battery. 



Now suppose that we wanted something different: Lamp 1 to be 
lighted at switch position 1; both lamps 1 and 2 to be lighted at switch 
position 2; and all three lamps to be lighted at switch position 3. How 
shall we do this? 

Here is the point at which we begin to make use of the power of 
the multiple switches in the kit: we have to use switching circuits 
more elaborately. Let us consider Experiment 8. 



Experiment No. 8 . INSTALLING A SWITCH DISC TO SWITCH ANY 
ONE OF THREE OVERLAPPING CIRCUITS 

You will need: Your Experiment No. 7; and additional hard- 
ware; you will see what is needed from looking closely at Figure 6. 

In this circuit we light Lamp 1 from position 1, both Lamps 1 
and 2 from position 2, and all three Lamps from position 3. 




Switch 



Battery 



Figure 6 



19 



Results and What happened: At Position 1, the only path that 
electricity can take is through Lamp 1, because only Jumper J can 
close a circuit. At Position 2 however Jumpers J and K both close 
circuits and so both Lamps 1 and 2 light. And at Position 3, all 
three Jumpers J, K, and L close circuits, and so all three Lamps 
light. 



Now before we go ahead with the last of these nine preliminary 
experiments in this booklet, we need to talk about the electrical con- 
tacts produced by the multiple switch. So long as we have only three 
jumpers in a switch disc, it is rather easy for all three of them to 
make contact at the same time; in the same way, it is easy for a 
three-legged stool to sit steadily on an uneven floor. But as soon 
as we have circuits with four or more jumpers required in the mul- 
tiple switch, we are likely not to have good electrical contact at all 
the points that we need contact, — in the same way as a table with 
four, five, or more legs may be unsteady on an uneven floor. 

To overcome this obstacle, we make use of the wipers, which 
have been patented (U. S. Patent No. 2848568). They provide more 
electrically connecting springiness between the switch base in the 
panel and the switch top in the disc. 

A wiper is a springy piece of phosphor bronze with a hole and 
two small ridges. The shape of the wiper unbent, as it comes in the 
small envelope, is shown in Figure 7. The purpose of the wiper is 
to improve the electrical contact between the top of the switch (the 
disc containing the jumpers) and the bottom of the switch (the panel 
containing the bolts and nuts for the terminals). 

The way in which the wiper is assembled is shown in Figure 8, 
and is as follows: (1) thread the bolt through the wiper, with its 
ridges down; (2) fasten the bolt not too tightly to the panel; (3) align 
the wiper with the spoke (or radius) of the switch; (4) now fasten the 
bolt tightly; (5) bend the wiper gently upwards and over the bolt, with 
the ridges up, in such a way that the wiper will slide neatly on the 
jumper, resting in its valley between the ridges; (6) assemble the 
multiple switch with a hard washer between the disc and the panel; 
(7) adjust the amount of bending of the wipers so that they push up 
and down nicely against the jumpers as the switch turns. 

In order for the switch to stay in a position to which it is turned, 
-20 - 



the body of the jumper must be in line with a spoke, and the valleys 
between the ridges on the wipers must be in line with the spoke; then 
the jumpers will have a tendency to catch in the valleys, as they 
should, to hold the switch in position (see Figure 8, end view). 

For multiple switches with only two jumpers evenly spaced, or 
only three jumpers almost evenly spaced, you will not need wipers 
and should not use them, for such switches will work entirely pro- 
perly without wipers. In these cases, you will need to make sure 
that the slots in the heads of the bolts are lined up with the spoke, so 
that the jumpers themselves will position (or detent) along the spoke 
right above the bolts. (In assembling a switch without wipers, you 
may not need the hard washer at the center. ) For switches with four 
or more jumpers, you will need wipers, for otherwise the switch is 
likely to work unreliably. 

Hole 



* 



; Ridges 




Wiper, ridges down 
Top view End view 

Figure 7 — Unbent wiper 



wiper - 
bent 



^ A * 



- disc - 
-jumper ■ 



Ridges of 
wiper 




■ wiper bent 

panel 



bent \j^^jt- 



Valley 
of wiper 



bolt 



Side view 



End view 



Figure 8 — Assembly of wipers 



21 



Experiment No. 9 . 



INSTALLING A SWITCH DISC TO SWITCH ANY 
ONE OF FOUR OVERLAPPING CIRCUITS 



You will need: Your Experiment No. 8; and additional hard- 
ware (including wipers), as you will see from looking closely at 
Figure 9. Every bolt which is a terminal in the multiple switch 
base will need to have a wiper, placed between the head of the bolt 
and the panelboard. 

In this case, we want the circuit to light Lamps 1 and 2 from 
Position 1, Lamps 1 and 3 from Position 2, Lamps 1, 2, 3, and 4 
from Position 3, and Lamps 2 and 4 from Position 4. 



Lamp 2 




Lamp 1 (This wire goes to lamp 1, but to make 
e. — " "" the diagram simpler it is not drawn) 



Pointer 




Battery 



Lamp 3 



You will have need of 20 wipers, one under the head of the bolt 
of each of the terminals shown by a black dot in the diagram. 

Results and What happened: As you can see from the diagram, 
and from operating your machine (after all the "trouble" has been 
"shot"), electricity can flow only to achieve the specified result. 
For example, at position 4, only Lamps 2 and 4 are lighted, for at 
that time the machine cuts off Lamps 1 and 3. 



Now suppose we wanted to assemble a multiple switch which 
could have any one of three positions A, B, and C, and which would 



-22 



be capable of switching every one of six different circuits. A way 
in which that switch could be assembled is shown in Figure 10. Six 
jumpers are inserted in the top of the switch, shown as y///a in Fig- 
ure 10. (It is important that jumpers ordinarily be inserted in pairs 
opposite each other, for reasons of mechanical balancing, so that 
the top of the switch will stay parallel to the bottom of the switch. ) 
A total of six times six or 36 nuts and bolts are inserted in the bot- 
tom of the switch, in the spots marked ^ in Figure 10. They are 
in groups of six called decks (also called poles , or levels ); these 
decks are electrically independent, and they enable us to switch 6 
different circuits at one time. In the base, the bolts belonging to 
any one deck in Ring 1 or Ring 3 are connected together by wire, as 
shown by the heavy line. They are made electrically common; in 
other words, they are commoned . Together they constitute what is 
called a transfer contact. 




Figure 10 — Three position switch, six decks (or poles or levels) 



Note that in drawings of the multiple switches, the rings and 
spokes may be drawn as thin lines; these lines are not actually drawn 



- 23 - 



on the switch discs nor the switch bases, nor do they represent el- 
ectrical lines connecting terminals; instead they are drawn to make 
the arrangement clearer and more evident. 

Let us now consider the layout of the 16 spokes and the 4 rings 
and the 64 holes which they produce. We can see that we can assemble 
a multiple switch in a great number of different ways. This is the ad- 
vantage of the design of the multiple switch we have patented. 



Here are the types of switches that can be made: 





Maximum 


Number of Positions 


Number of Decks 


2 


16 


3 


10 


4 


8 


5 


6 


6 to 8 


4 


9 to 16 


2 



Even more variations are possible under some conditions. 



CERTIFICATE OF ACHIEVEMENT 

(to be filled in by the young scientist if he has correctly 

completed all nine electrical research experiments) 

Date 



has correctly complet- 



(Your Name) 
ed as of this date the nine electrical research experiments in 
Booklet 1 of the Brainiac K20 kit, and is to be commended for 
his achievements. He is now qualified to assemble the com- 
puting and reasoning machines described in Booklet 2. If he 
completes Booklet 2 with equal care and diligence, he has the 
qualities of a true scientist, and it is predicted that he will 
eventually design his own machines, first with this kit, and 
later with more complicated kits. In fact, it is not unlikely 
that he will make his career in the field of electricity and 
modern science. 



24 - 



GENIACS: 

SIMPLE ELECTRIC BRAIN MACHINES, 
AND HOW TO MAKE THEM 



Also: 
Manual for Geniac Electric Brain Construction Kit No. 1 



Edmund C. Berkeley 



Copyright 1955 by Edmund C. Berkeley 



Published March 1955 by Berkeley Enterprises, Inc., 
36 West 11 St., New York 11, N. Y. 



Introduction 



In 1944 the first "electric brain", an automatic machine 
for reasoning and calculating, began to work. In the years 
since then, more and more people have studied and built machines 
that handle information in reasonable ways, machines that "thiik" 
or at least seem to think. Thousands of such machineshave now 
been made. This development is becoming so important that it 
is often called the Second Industrial Revolution. 

Since 1945 we have been interested in helping people un- 
derstand these machines and ^ow they behave. And we know that 
equipment that you can take into your own hands, play with, and 
do exciting things with, will often teach you more, and give 
you more fun besides, than any quantity of i/ords and pictures. 

In 1950, for educational purposes, we constructed a mini- 
ature electric brain called Simon. Although only 1% cubic feet 
in size, and limited in capacity, it was a complete automatic 
computer, and it could show how a machine could do long se - 
quences of reasoning operations. The picture of Simon ha s 
appeared on the front cover of two magazines, "Scientific 
American" and "Radio Electronics"; the machine itself has 
been demonstrated in more than eight cities of the United 
States. Over 350 sets of Simon plans have been sold. But 
this machine costs over $300 for materials alone, and is 
therefore too expensive for many situations in playing and 
teaching. 

The same summer that Simon was finished we began work to 
develop a really inexpensive electric brain. Now, four years 
later, we have gathered and worked out descriptions of over 
30 small electric brain machines, most of them simple, some 
of them complicated, and all of them interesting, which can 
be made with very simple electrical equipment. These machines 
are described in the first part of this report. 

In order to make the assembling of these small electric 
brain machines as easy as possible, we have also developed a 
construction kit costing less than $16 (in March, 1955) which 
will make any one of these little machines (with the exception 
that some of the machines require a few more nuts and bolts) . 
The name of the kit is "Ceniac Kit No. 1"; the word "Geniac" 
comes from the phrase "Genius Almost-Automatic Computer"; and 
we call the little machines that can be made "Geniacs". This 
report is also the manual for the kit; and the second part of 
this report describes the kit and how to assemble machines from 
it. 



2 - 



The kit contains basically: (1) the materials for six, 
all-purpose, multiple, electrical switches, of a new and ver- 
satile design, for calculating and reasoning; (2) ten flash- 
light bulbs, for signaling answers; and (3) one flashlight 
battery for power. Every Geniac, although unable to run auto- 
matically, is able to calculate and reason automatically; and 
the Geniac manual and kit as a whole demonstrate, many differ- 
ent and exciting small machines that "think", at least to the 
extent of reasoning and calculating. 

The kit, though inexpensive and convenient for construct- 
ing Geniacs, is however not necessary; and some persons will 
prefer to construct their Geniacs using other materials. We 
know however that the kit will make any one of more thai a 
hundred simple little electric brain machines. 

We hope that you find this report of interest to you, and 
that you will enjoy playing with the kit, and entertaining your 
friends with the little machines that you make. And when you 
work out new electric brain machines, send us the descriptions: 
we plan to give prizes fror time to time for the best ideas 
sent in to us. 

If you find you have at first some difficulty in under- 
standing all that is in this report: TAKE YOUR TIME and think; 
make first the simpler machines; then try the more complicat- 
ed ones. To make a machine that will reason and calculate , 
you, too, need to reason and calculate. 

In this report, in stating the design of a number of dif- 
ferent circuits, we have used a number of different styles of 
statement (several styles of drawings, lists of wiring instruc- 
tions, etc.) A reader may believe that we should have used 
one and only one style. Such uniformity of style is not prac- 
tical for two reasons. First, some circuits are simpler and 
easier to see in one style of statement, while others are sim- 
pler and easier to see in another style of statement. Second, 
the literature on circuits uses different styles of statement; 
and becoming accustomed to the different styles used here is 
a better introduction to the literature. 

We have had great help from several outstanding computer 
men in the design of about one third of the Geniac circuits 
described in this report. We express our thanks to them, and 
regret that they feel they have to remain anonymous. 

It is Loo much to hope that this report contains noerrors. 
We shall be very grateful to any reader who sends us correc- 
tions, and comments and suggestions for later editions of this 
report. 

8 _ 145(p30 Edmund C. Berkeley 



CONTENTS 



Part I : Simple Electric Brain Machines: 
General Description 

1. Flashlight 7 

2. Hall Light 8 

3. Doorbell 8 

4. Porch Light 9 

5. Burglar Alarm ' 10 

6. Automatic Oil Furnace Circuit 10 

7. Private Signaling Channels 11 

8. Machine for a Space Ship's Airlock 12 

9. The Fox, Hen, Corn, and Hired Man: the 

Farmer's Machine 14 

10. The Machine for the Two Jealous Wives 15 

11. The Machine for Douglas Macdonald's Will 16 

12. Special Combination Lock 17 

13. General Combination Lock 18 

14. Masculine-Feminine Testing Machine 

15. Adding Machine 20 

16. Subtracting Machine 20 

17. Multiplying Machine 21 
10. Dividing Machine 22 

19. Machine for Arithmetical Carrying 23 

20. Comparing Machine 24 

21. Reasoning Machine 25 

22. Intelligence Testing Machine 28 

23. The Uranium Shipment and the Space Pirates 3o 

24. Secret Coder 32 

25. Secret Decoder 32 

26. Machine to Play Nim 35 

27. Machine to Play Tit-Tat-Toe 37 

28. Translator from Binary to Decimal 40 

29. Translator from Decimal to Binary 42 

30. Binary Adding Machine 43 

31. Binary Multiplying Machine 44 

32. Binary Comparison Machine 45 

33. "Two -Out -Of -Five" Code Translator 46 



Part II: Materials in the Geniac Electric 47 
Brain Construction Kit, No. 1, and 
Explanation of Them 



- 4 - 



Part I: Simple Electric Brain Machines: 
General Description 



An electric brain machine is a machine containing elec- 
trical circuits which is able to calculate or reason, that is, 
perform operations that are reasonable or mathematical. For 
a simple example, consider a flashliqht. It performs a single, 
very reasonable operation: the light turns on when you turn 
the switch to the "on" position; and the light turns off when 
you turn the switch to the "off" position. 

The machines which we shall talk about will be made of: 
a battery, or source of electric current; wires, which conduct 
it; switches, which change the paths along which the current 
flows; lights, which show where the current is flowing. In all 
of these machines the current starts from one end of the bat- 
tery and flows in a path or circuit that eventually returns to 
the other end of the battery. 

The diagram of the circuit or circuit diagram shows th e 
scheme of connection of batteries, switches, lights, etc., in 
order that the machine will function as it is supposed to. The 
diagram does not necessarily show the physical location of the 
material but only its relative arrangement, its connections. 

The symbols used in circuit diagrams are shown in Table 1. 
We need pay attention only to five kinds of material. 



Table 1 
CIRCUIT DIAGRAM SYMBOLS 



I- 



~~L 



A battery. — The long and short 
lines supposedly represent the two 
kinds of plates in a battery by means 
of which an electrical curren t i s 
generated. 

Wire. — A line in a circuit diagram 
represents an insulated wire, a con- 
nector from some point to some other 
point. 



- 5 - 



/. . 



Electrical connections. — The dots 
represent points where electrical 
connections are established, by fas- 
tening two wires together so current 
can flow easily between them. 

No electric connection intended. — 
Here two wires cross (drawn in either 
one of two ways) but there is no el- 
ectrical connection between them . 
One wire is either above or below 
the other. 

A light. — This is a light bulb . 
The two dots are its connections. 

Switches. — Here is a two-position 
switch (drawn in either one of two 

ways) . 

Here is a three-position switch. 

Here is a four-position switch. Etc. 

Contacts. — In any switch, the con- 
tacts have names: 



/ 



/Transfer 
Contact 



Normally Normally 
Closed Open 
Contact Contact 



/ 



Transfer 



A single switch may be constructed having two or three or 
more electrically nonconnecting sections so that as it is turn- 
ed, it simultaneously switches two or three or more electri - 
cally independent paths. In circuit diagrams this property of 
a switch is conveniently shown by using a name for the switch 
and numbers 1, 2, 3, etc., for the sections. In Figure 1 for 
example two, not three, switches are shown: diagram (a) repre- 
sents section 1 of the switch called ''Wife", diagram (b) pic- 
tures section 2 of the same switch, and diagram (c) shows sec- 
tion 1 of the switch called "Husband". Sometimes a section of 



- 6 - 



a switch is called a deck or a pole or a level . In Figure 1 
both switches have the same two positions, called "in canoe" 
and "not in canoe". 



Not 





Wif< 






Wife 




Hus 




-1 


-2 


V 




/ 






/ 






/ 





In 
canoe 



(a) 



(b) 



(c) 



Figure 1 — Switches, Names of Switches, 
and Names of Positions 



With these preliminaries out of the way, let us consider 
the first machine. 



1. THE FLASHLIGHT 

Problem : A man desires to make a flashlight, which will 
shine when he turns the switch on, and go dark when he turns 
the switch off. 

Solution : This is accomplished in the following circuit: 

1 Switch 

Battery — Off < 1 On 

Light 



The circuit is regularly drawn with all switches in the off or 
or zero position . As it is drawn, we can see that no current 
will flow, because there is a gap; so the light will be off. 
But when the switch is turned to the on position, then the cir- 
cuit diagram will be as follows: 

Switch 



X 



Battery — 



Off; 



On 
(J) Light 



,We see that current will now flow and the light will shine. 
(For the detailed wiring using the kit materials, see p. 59) 



- 7 



2. THE HALL LIGHT 



Problem : A man desires to turn off or turn on the down- 
stairs hall light either from the downstairs hall or from the 
upstairs hall. He wants a circuit so that if either switch is 
turned, the light will go on if it was off, and will go o f f 
if it was on. 

This is a practical problem, if you should ever 
have to install this kind of wiring. And it is not as eas y 
as it may seem at first glance. 

Solution: Here is the solution expressed in a circuit 
diagram: 



Battery- 



^r 



Upstairs Switch 
Position B , *| f — , Position A 



3 



Position B I $ 4. — 1 Position A 

Downstairs Switch 
Hall Light 



We can see that if both switches are turned to Position B, 
then the light will shine. If both switches are turned to 
Position A, then the light will also shine. If only one switch 
is in Position A and the other switch is in Position B, the n 
the light will not shine. This circuit therefore meets the 
requirements. (For detailed wiring, see p. 60) 

3, THE DOORBELL 



Problem : A man has four doors to his house, a front door, 
a back door, a side door, and a door to the garden. If any- 
one comes to any of these doors, and rings, the doorbell shouii 
ring. What is a circuit that will accomplish this? 



Solution: 



Front Door 



<HR 



Silent 
(S) 



Back Door 



<H 



Side Door Garden Door 



Q^) Doorbell Ringing 



Ring 
(R) 



We can see that if all four switches are in the positio n 
"Silent", the path is interrupted, and the light that means 
"Doorbell Ringing" will be dark. But if any one or more of the 
switches is turned to the "Ring" position, then the light mean- 
ing "Doorbell Ringing" will shine. (For detailed wiring, see 
p. 61) 

4. THE PORCH LIGHT 

Problem: A man has a light on his front porch which lights 
up his front steps and his yard. He wants to be able to turn 
that light on or off from any one of three places: his down- 
stairs front hall (H) , the upstairs landing (U) , and the attic 
(A) . Three switches are to be put in and wired so that throw- 
ing any switch one way turns the light on if it is off, and 
turns the light off if it is on. 

Solution: Here is the circuit. Note that the upstairs 
switch, Switch U, must have two decks, two sections. 



4 <- 



S=r 



Peck I 






4 <-■ 



<§> 



Upstairs Switch Attic Switch 

U A 



Hall Switch 
H 

The two decks in the upstairs switch are mechanically fastened 
together so that when the switch is turned, the two transf e r 
contacts in Deck 1 and in Deck 2 are both turned. Otherwise 
the circuit would not work. (For detailed wiring, see p. 61) 



THE BURGLAR ALARM 



Problem : A man has two doors to his house, and two large 
windows on the ground floor. He believes that if a burglar 
should try to enter his house, the burglar would come in through 
one of the doors or one of the big windows. He desires an a- 
larm system. If either door is opened or if either one of the 
two big windows is opened, after either one of two locking 
switches (one indoors for use at night, one outdoors in the 
garage for use when the house is left with no one in it) has 
been closed, then the burglar alarm is to ring. 

Solution : We shall need six switches labeled Lock One, 
Lock Two, Door One, Door Two, Window One, Window Two. Each wil 
be a two-position switch, and only one deck of each switchwill 
be used. Following is a circuit: 



iw\ 



Ch 055 



Lock 3l 



On Otf 



Wcnc^ovv \ Wi-hdow>J 



SWt Ope* Shell OpJ Shut Ope* 



Shut Open 



fi La r w d) 



In reality, each door and window must be closed shut against 
a button containing a strong spring, so that when the door or 
window is opened, the spring pushes the button out and closes 
a contact. (For the detailed wiring, see p. 62) 

6. THE AUTOMATIC OIL FURNACE CIRCUIT 

Problem: A man has an automatic oil furnace which burns 
oil and makes water into steam to heat the radiators in the 
house. The flame starts when the thermostat in his living 
room calls for heat, and stops when the thermostat stops call- 
ing for heat. But if any one of the following conditions ex- 
ists, the furnace is not allowed to heat: 

— the chimney is too hot 



- 10 



— the pressure in the boiler is over 15 pounds per 

square inch above atmosphere 

— the fuel in the tank is too low 

— the blower that mixes air with oil and blows the 

mixture into the furnace is not working 

— the water level in the boiler is below a certain 

mark. 

Set up a circuit which will imitate the behavior of the auto- 
matic oil furnace. 



Solution : The front of the panel will look like this: 

Heat Wanted / ^— >^ Too hot >**-^Too high 

•Not too hot \^y° K 
Thermostat Chimney Pressure 



V^^Vno heat wanted\^_jyN 



Too low 
Fuel 



@ 



C^w Not working / ^ ra *^Too low 
Blower Water Level 



Light that 
shows Furnace is Burning 

The circuit is as follows . (NOTE: Here o denotes "source of 
current" or "one side of battery"; "dr denotes "sink of cur- 
rent" or "ground" or "other side of battery"; these are com - 
mon symbols.) 




Thermostat, Heat 
wanted 

Chimney too hot 

Pressure too high 



(t) 



I A Fuel too low 

} Blower not working 
Water level too low 



Furnace Burning 



7. PRIVATE SIGNALING CHANNELS 

Problem : Set up a machine so that each one of three boys, 
George, Tom, and Dick can signal any one of the other two. 

Solution : We shall have three switches, one for each boy. 
Each switch will have two settings, one for each other boy . 



- 11 - 



There will be six lights, indicating who is signaling and who 
is being signaled. 

The wiring will be as follows: 

1. Wire from one end of the battery to the trans- 

fer of one deck on each switch, 

2. Wire from the outputs of each switch to the 

lights, as follows, and from the other side 
of the lights back to the other end of the 
battery. 

Switch Output Light 

George Tom George calling Tom 

Dick George calling Dick 

Tom George Tom calling George 

Dick Tom calling Dick 

Dick George Dick calling George 

Tom Dick calling Tom 

NOTE: In this case, instead of furnishing a circuit diagram, 
we have. given a statement of the circuit in the form of a set 
of wiring instructions. This is logically equivalent, and 
often in practical situations a good deal better. 



8. MACHINE FOR A SPACESHIP'S AIRLOCK 

Proble m: The airlock of a space ship has: an inner door 
that goes from the airlock to the inside of the space ship; an 
outer door which goes from the airlock to the surface of the 
strange planet, which is assumed to have no atmosphere; a pump 
which pumps the air from the airlock into the space ship; a 
valve which allows air from the space ship to flow into the 
airlock; and a pressure gage which reports the air pressure in 
the airlock and which may be either high or low. There are 
four lights in the airlock: safe to open the inner door; safe 
to open the outer door; dangerous to open either door, condi- 
tions OK; dangerous to open either door, conditions bad. We 
want,a warning circuit and automatic locks corresponding. 



- 12 - 



Solution : The front of panel will look like the follow- 
ing: 

Gage . 
Valve from Pump from showing Pressure 

Spaceship to Airlock Airlock to Spaceship in Airlock 




shut 



open 




Light 1 : 



■© 



Safe to open the inner 
door; automatic lock of 
outer door 



Light 3 : 



© 



Dangerous to open either 
door; automatic lock of 
both doors; conditions OK 



off 



Light 2 




full 
pressure 

zero 



: ® 



Safe to open the outer door; 
automatic lock of inner 
door 

Ligh 



iflM 4: (T\ 



Dangerous to open either 
door; automatic lock of 
both doors; conditions bad 



The circuit is as follows: 




13 - 



9, THE FOX, HEN, CORN, AND HIRED MAN: THE 
FARMER 'S MACHINE 

Problem : A farmer had a fox t a hen, some corn, and a 
hired man, and two barns, where one or more of them could be 
at any one time. He did not trust his hired man's carefulness, 
He wanted a warning robot to shine a danger light (1) when the 
fox was with the hen in either barn, the hired man being in 
the other barn, and (2) when the hen was with the corn in eith- 
er barn, the hired man being in the other barn, and a safety 
light on other occasions. 

There will be a switch for the hired man (M) , a switch 
for the fox (F) , a switch for the hen (H) , and a switch for the 
corn (C) ; and one position of each switch will mean "it is in 
Barn 1" and the other position will mean "it is in Barn 2". 

Solution: Here is the circuit: 



r4^7k 



Battery 



Barn 1: 
position 
on the 
left 



Safety 
Light 




Barn 2: 
position 
on the 
right 



Danger 
Light 



- 14 



10. 



THE MACHINE FOR THE TWO JEALOUS 
WIVES 



Problem : One summer two families vacation in neighbor- 
ing bungalows on the shore of a pleasant lake. The two wives 
are jealous, and one day agree that the husband of either one 
may not go canoeing alone with the other wife, unless accom- 
panied by a chaperon. They also believe that the chaperon 
might be more attractive than they would wish, and consequent- 
ly they agree that neither husband should go canoeing alone 
with the chaperon. 

They arrange with an electrician to set up an apparently 
innocuous wiring system in the boat house, and they arrange 
with the boat boy to turn switches to show who is out in the 
canoe. In their living rooms, they arrange a danger light to 
shine when the situation is contrary to their agreement, and 
a safety light to shine on all other occasions. 

How should the circuit be wired? 

There are five two-position switches marked Husband One 
(Hi), Husband Two (H 2 ) , Wife One (Wj) , Wife Two (W 2 ) , Chaperon 
(C) . One position I stands for "in the canoe". The other po- 
sition N stands for "not in the canoe". 



Solution : Following is a circuit which will work. The 
decks of each switch are numbered; thus C-3 is the 3rd deck 
of the Chaperon switch. 



Position "Not 
in the Canoe" 
to the left 



(For detailed wiring, see p 




Position 
"In the Canoe" 
to the right 



Safety 



- lb 



11. 



THE MACHINE FOR DOUGLAS MACDONALD'S 
WILL 



Problem : The provisions of Douglas Macdonald 's will are 
as follows: "If my son Angus survives me and my son Brian does 
not, all my estate goes to Angus. If Brian survives me and 
Angus does not, all my estate goes to Brian. If neither sur- 
vives me, my estate is to go to the Gaelic Home for the Aged 
and Indigent. If both Angus and Brian survive me, and if at 
the time of my death neither is married nor is a graduate of 
Edinburgh University, then each shall have 50% of my estate. 
If both are married and neither is a graduate, or if both are 
graduates, and neither is married, or if both are married and 
both are graduates, then each shall have 50% of my estate. If 
only one of my sons is a graduate, his share shall be increas- 
ed by 20% of my estate and the other's decreased accordingly. 
If only one of my sons is married, his share shall be increas- 
ed by 10% and the other's decreased accordingly." What hap- 
pens when Douglas Macdonald dies? 

We wire up a circuit having six switches showing all the 
conditions for Angus and Brian (living or not, graduate or not, 
married or not) and ten output lights, showing what happens in 
any one of the 64 possible events. 

Solution : Following is the circuit: 

No J Yes 

*! ^ — j£ (Angus) Living 

(Brian) Living 



Yes |No 

] t0 <$> &> 

ian -£ x. 



[No Yes|j\ 



Al 
Brian ^ 



All to Gaelic 
Home 



fe 



No' 



No^Yes I nio« 




All to Angus 
A Graduate 



Yes 



for 



Yes 



^o 



Yes 



Yes 



"No I Ye 



T 



"No 



20 30(|) 40(|=) 50 &) 60 70 80 



Lights show percent to 



Yes ' 



No 



B Graduate 



Y^s" 



No 



— > F — 
Yes No 



A Married 



B 
Married 



Angus 



16 



12. THE SPECIAL COMBINATION LOCK 

Problem: Set up a machine with the following properties: 
each one of three switches may be set at any digit from to 
9; when and only when the first switch is set at 5 t the sec- 
ond digit at 6, and the third digit at 3 f a light "Open" will 
glow. 

Solution: Here is the circuit: 




First Digit 



Obviously, the combination can easily and quickly be changed 
by altering the location of a wire or two. 



17 - 



13. THE GENERAL COMBINATION LOCK 

Problem : Set up a machine with the following properties: 
you may use any three digit combination with digits 1 to 9 on 
three switches; when and only when three more switches are set 
with the same combinations but each digit one less, a light 
"Open" will glow: 



Solution : Here is the circuit: 
COMBINATION 




Digit 1 



18 - 



14. MASCULINE-FEMININE TESTING MACHINE 



Problem : Set up a machine which will determine whether 
the person who answers five questions (if he or she answers 
them truthfully) is more masculine or more feminine: 



1. 

2. 

3. 



Whom do you prefer: (a) Marilyn Monroe? (b) Liberace? 

How would you put a thread into a small hole: (a) wet it? 
(b) tap it? 

Which would you agree with? (a) Women are better drivers 
than men because they are more careful, (b) Men are bet- 
ter drivers than women because they get more practice 
and are more skilled. 

Would you rather spend a day: (a) Shopping on Fifth Avenue? 
(b) Hunting in the woods? 

Which makes a better toy for a child: (a) electric train? 
(b) a doll with a complete wardrobe? 

Solution : Following is the circuit. 



Marilyn Monroe 
Wet 
Women Better 



Oues. 1 
Liberace 

Oues. 2 
Tap It 

Oues. 3 
Men Better 




More Feminine 



*' Electric Train 



More Masculine 



- 19 - 



15. ADDING MACHINE 

16. SUBTRACTING MACHINE 

Problem: We have two switches A and B, each able to be 
set at any one of four positions 5 f 6, 7, 8. We have seven 
lights labeled 10, 11, 12, 13, 14, 15, 16. We want a circuit 
so that the machine will show the sum of the numbers set on 
the A and B switches. 

Solution : Here are the wiring instructions: 

1. Wire one end of the battery to the transfer on one deck 

of switch A. This deck of switch A has four outputs 5, 
6, 7, 8. 

2. Wire each one of these four outputs to each one of four 

transfers on switch B, one on each deck. Call these 
decks 5, 6, 7, 8, according to the A output wired to it. 
Now switch B will have sixteen outputs. 

3. Wire these outputs to one side of the lights according to 

the following table of instructions (use column (1) ) . 



Deck 


B output 


Liqht 


Liqht 


5 


5 


10 


-3 




6 


11 


-2 




7 


12 


-1 




8 


13 





6 


5 


11 


-2 




6 


12 


-1 




7 


13 







8 


14 


1 


7 


5 


12 


-1 




6 


13 







7 


14 


1 




8 


15 


2 


8 


5 


13 







6 


14 


1 




7 


15 


2 




8 


16 


3 



4. Wire the other side of each light to the other side of the 
battery. 

- 20 - 



Notes: (1) Any four consecutive numbers and their sums can be 
substituted, using other labels; and the machine will still 
work correctly, (2) The machine will work as a subtract i n g 
machine giving A minus B if the positions of the B switch are 
labeled 8 f 7, 6, 5, instead, and the lights are labeled a s 
shown in column (2) above, instead. 



17. MULTIPLYING MACHINE 

Problem : We have two switches A and B, each able t o b e 
set at four positions 6, 7, 8, 9. We have ten lights labeled 
36, 42, 48, 49, 54, 63, 64, 72, 81. We want a circuit so that 
the machine will show the product of the A and B numbers set 
on each switch, by shining the appropriate light. 

Solution : Here are the wiring instructions: 

1. Wire one end of the battery to the transfer on one 

deck of switch A. This deck of switch A has four 
outputs 6, 7, 8, 9. 

2. Wire these four outputs to each one of four transfers 

on switch B, one on each deck. Call these decks 6, 
7, 8, 9 according to the A output. Thus switch B 
will have sixteen outputs. 

3. Wire these outputs to the lights according to the fol- 

lowing table of instructions: 



Deck B Output Light 



6 


36 


7 


42 


8 


48 


9 


49 


6 


42 


7 


49 


8 


56 


9 


63 



Deck B Output Light 



a 



6 


48 


7 


56 


8 


64 


9 


72 


6 


54 


7 


63 


8 


72 


9 


81 



- 21 



4. Wire the other side of each light to the other end of 
the battery. 

Note : This same machine can be relabeled according to the 
following system, and will still tell the truth: 



6 7 8 9 


36 42 48 49 54 56 63 64 72 81 


2 3 4 5 


4 6 8 9 10 12 15 16 20 25 



In fact any four consecutive numbers, none smaller than 2, 
and their appropriate products can be inserted. 



18. DIVIDING MACHINE 

Problem : We have two switches, A and B, each able to be 
set at any one of 0, 1, 2, 3. We have ten lights labeled 0, 
1/3, 1/2, 2/3, 1, V/ 2 , 2, 3, 00, ? We want a circuit so that 
the machine will show the quotient of A divided by B, where A 
and B are the numbers set on the switches. 

Solution : Here are the wiring instructions. 

1. Wire one end of the battery to the transfer on one 

deck of switch A. This deck of switch A has four 
outputs 0, 1, 2, 3. 

2. Wire each one of these four outputs to each one of 

four transfers on switch B, one on each deck. Call 
these decks 0, 1, 2, 3 according to the A output 
wired to it. Now switch B will have 16 outputs. 

3. Wire these outputs to one side of the lights according 

to the following table of instructions: 



Deck 


B Output 


Liqht 








? 




1 







2 







3 





1 





oo 




1 


1 




2 


1/2 




3 


1/3 



22 



xjc 


B Output 


Liqht 


2 









1 


2 




2 


1 




3 


2/3 


3 









1 


3 




2 


1% 




3 


1 



4. Wire the other side of each light to the other side of 
the battery, 

19. MACHINE FOR ARITHMETICAL CARRYING 

Problem : We have two switches, A which may be set at any 
one of the numbers 3 f 4, 5, 6 and B which may be set at any one 
of the numbers 2 f 3 f 4 t 5, 6, 7. We have two lights Carry One, 
and No Carry, We want a machine so that these lights will b e 
turned on properly. 

Solution : Here are the wiring instructions. 

1. Wire one end of the battery to the transfer on one 

deck of switch A. This deck has four outputs 3, 4, 
5, 6, 

2. Wire each one of these four outputs to the transfer 

of each one of four decks of switch B. Call these 
decks 3 f 4, 5 f 6 according to the A output wired to 
it. 

3. Wire the outputs of the B switch to one side of the 

lights as follows: 



Deck B Output Liqht Deck B Output Liqht 

3 7 Carry One 5 5 to 7 Carry One 
2 to 6 No Carry 2 to 4 No Carry 

4 6, 7 Carry One 6 4 to 7 Carry One 
2 to 5 No Carry 2,3 No Carry 



23 



4. Wire the other side of the lights to the other end of 
the battery. 

Note : Similar machines may be made for other cases of 
arithmetical carrying. But relabeling this machine for other 
cases of carrying is not likely to work out very well. 



20. COMPARING MACHINE 

Problem : We have two switches A and B, each able to b e 
set at any one of four numbers 6, 8 t 10 t 12. We have three 
lights labeled GREATER, EQUAL, LESS. We want a circuit that 
will show whether A is greater than B t or A is equal to B, or 
A is less than B, where A and B are the numbers set on the 
switches. 

Solution : Here are the wiring instructions. 

1. Wire one end of the battery to the transfer of one 

deck of switch A. This deck of switch A has four 
outputs 6, 8 t 10 and 12. 

2. Wire each one of these four outputs to just one of 

four transfers on switch B, one on each deck. Call 
these decks 6 f 8, 10 t 12 according to the A output 
wired to it. 

3. Wire these outputs to one side of the lights accord- 

ing to the following table of instructions: 

Deck B Output Light 



10 



6 


E 


8 


L 


10 


L 


12 


L 


6 


G 


8 


E 


10 


L 


12 


L 


6 


G 


8 


G 


10 


E 


12 


L 



24 



Deck 


B Output 
6 


Ligl 


12 


G 




8 . 


G 




10 


G 




12 


E 



4. Wire the other side of the lights to the other end of 
the battery. 

Note : This same machine can be relabeled using any other 
four numbers in sequence. 



21. REASONING MACHINE 

Problem : Switch A can be set at any one of these four 
positions: 

1. All fighter pilots are bomber pilots. 

2. No fighter pilots are bomber pilots. 

3. Some fighter pilots are bomber pilots. 

4. Some fighter pilots are not bomber pilots. 

Switch B can be set at any one of these four positions: 

5. All bomber pilots are jet pilots. 

6. No bomber pilots are jet pilots. 

7. Some bomber pilots are jet pilots. 

8. Some bomber pilots are not jet pilots. 
We have six lights: 

9. All fighter pilots are jet pilots. 

10. No fighter pilots are jet pilots. 

11. Some fighter pilots are jet pilots. 

12. Some fighter pilots are not jet pilots. 



13. Some jet pilots are not fighter pilots. 

14. It is not possible to deduce from the given statements 

any true assertion connecting fighter pilots and jet 
pilots. 

We want a machine which will reason correctly. 

Solution : Here are the wiring instructions. 

1. Wire one end of the battery to the transfer on one 

deck of switch A. This deck of switch A has four 
outputs, l t 2, 3, 4. 

2. Wire outputs l t 2 t 3 to just one of three transfers 

on three separate decks of switch B, one on each 
deck. Call these decks 1, 2 t 3 according to the A 
output wired to it. Now switch B will have 12 out- 
puts. 

3. Wire these twelve B outputs and the A 4 output to one 

side of the lights according to the following table 
of instructions, and wire the other side of the lights 
to the other end of the battery. 



Deck 


B output 


Liqh- 


1 


5 


9 




6 


10 




7 


14 




8 


14 


2 


5 


14 




6 


14 




7 


13 




8 


14 


3 


5 


11 




6 


12 




7 


14 




8 


14 


A output 






4 




14 



Note : The following replacements of fighter pilots (a 's), 
- 26 - 



bomber pilots (b's), and jet pilots (c 's) , may be made if de- 
sired and the same machine will reason correctly: 



b's cl 



baseball players football players basketball players 

associates colleagues followers 

flesh eaters leaf eaters grain eaters 

merchants traders dealers 

clients customers patrons 

pastry cooks barbecue cooks regular cooks 

etc.. etc. 



27 



22. INTELLIGENCE TESTING MACHINE 

Problem : Following are six questions, each with five 
answers, only one of which is correct: 

1. What is the middle letter of a nine-lettered word 

meaning an instrument for talking over a distance 
along a wire? 

( )T ( )G ( )R ( )P ( )F 

2. The statement "I wonder how he earns his living?" in- 

dicates what on the part of the speaker? 

( ) Amusement ( ) Jealousy ( )Curiosity 
( ) Eagerness ( )Meditation 

3. Which of the words below does not belong in the list? 

( ) Herder ( ) Cowboy ( ) Gardener 
( ) Keeper ( ) Shepherd 

4. Wit is to dullness as approval is to: 

( ) Respect ( ) Improvement ( ) Flattery 
( )Disliking ( )Disproving 

5. If the words below were arranged to make the best 

sentence, with what letter would the last word o f 
the sentence end? 

ax good keeps sharp lumberjack his a 

( )P ( )K ( )X ( )S ( )A 

6. Which of the following words makes the truest sentence? 

A mother is always than her daughter. 

( ) Bigger ( ) Older ( ) Calmer ( ) Younger 
( ) Wiser 

Solution : This problem uses six switches. The front of 
the board with the switches labeled on it will look like the 
following: 

7 s~% kI% s-^ v^v-n*, 

Question 1/ YlQuestion 2/ \ Question 3 j ^q 

\J? v3 V^tf 

Question 4 Question 5 Question 6 

- 28 - 



V 



The desired machine will score the test, and show in seven 
lights from to 6 the number of correct answers. 

The correct answers to the questions are these: 1 - P; 
2 - C; 3 - G; 4 - Disliking; 5 - P; 6 - 0. On the other side 
of the panel mark with 1 the position of the switch that shows 
this answer. Connect together the other four positions of the 
switch (on the other side of the panel) and mark them 0. We 
now have the equivalent of a two-position switch. 

The circuit which will give the correct number of answers 
is now displayed below: 

Switch Position to the right, 1 
Ques. 1 Position to the left, 

2 (2 decks) 
ues. 3 (3 decks) 

Ques. 4 (4 decks) 

Ques. 5 (5 decks) 
^j < 1 Ques. 6 (6 decks) 




<k) (pi k)2 (&3 (£)4 (|)5 (4)6 



Notes : This machine can be used for any kind of 6-questio n 
intelligence test changing a few wires so that differently 
located alternatives are the correct answers to the questions . 



29 



23. THE URANIUM SHIPMENT AND THE SPACE PIRATES 

Problem . A uranium shipment from one of Jupiter's Moons, 
Callisto, to Earth consists of a freighter rocket ship loaded 
with uranium and a fighter escort rocket ship disguised as a 
freighter. Space pirates are known to be lurking on one of the 
two asteroids, Pallas or Hermes, The pirates suspect that one 
of the rocket ships is a disguised fighter; therefore they may 
either attack the first ship or wait in hiding for a seco n d 
ship. The commander of the uranium shipment can send either 
ship by the Pallas or the Hermes route and can send the fighter 
either first or second. If the pirate attacks the fighter, the 
pirate will be destroyed. If the pirate attacks the urani u m 
ship and the fighter has already passed or taken the ot h e r 
route, then the pirate captures the uranium. If the pi rat e 
attacks the uranium ship, and the fighter is taking the sam e 
route, and is behind the uranium ship, the pirate is destroyed 
but during the battle, the pirate destroys the uranium ship . 
Of course, if the pirates do not attack, there is no combat. 

What happens to the uranium shipment? 

Solution . There will be five two-position switches to ex- 
press either one of the two possibilities for each of the five 
conditions : 

1. Pirates lurking on Pallas or Hermes (1 deck) 

2. Fighter travels via Pallas or Hermes (2 decks) 

3. Uranium shipment travels via Pallas or Hermes 

(4 decks) 

4. Fighter travels first or second (2 decks) 

5. Pirate attacks first ship or waits for seco n d 

ship (8 decks) 

There will be four lights to express any one of the four 
possible outcomes: 

1. Pirates destroyed, uranium shipment safe 

2. No combat 

3. Pirates and uranium shipment both destroyed 

4. Pirates capture the uranium 

Following is the circuit: 



30 



Current 



Switch 3 Switch 4 Switch 5 

o o 'o- 



,itch2? Tc |'° j 

nPO— -O H O— tbln 




Light 4: 
Pirates cap-- 
ture the ura-~ 
nium 

Note : In this case another way of showing the wiring 
of the switches has been used. The set of terminals on the 
switches has been shown as a column of pairs of small cir- 
cles, and the two positions of the switches have been desig- 
nated with letters or numbers. 



31 



24. SECRET CODER 

25. SECRET DECODER 

Problem . Set up a machine which will encipher a message t 
putting it into cipher, and which can also be used to decipher 
the message, putting it back into plain text. 

Solution . Following is the wiring for a machine whic h 
will do this: 



Switch 1 



M 6 

L o 

K I 
J 

I o 
H I 
G 
F 

E 
D 
C 
B 

A 



O 

O- 



"Correct" 
Light 



Switch 2 
(1) 



>^o- 



(2) 

N 

P 



R 

S 

T 

U 
V 

w 

X 
Y 



Each of these two switches is a switch with one deck and 13 
positions. The lamp signals when the pairing of letters is 
correct. The sign W7Z\ designates the jumper. 



32 - 



This machine will both encipher and decipher a message. 
To encipher, set a letter from the message on whichever dial 
it occurs. Then turn the other dial until the lamp lights. 
Use the letter from the second dial for the code message. The 
same process decodes the message. 

The labels in column (1) give a Caesar-type Cipher, so 
called because this type was used by Julius Caeser. 

Here are some messages in the Caesar Code for you to de- 
cipher: 

JR NER FHEEBHAQRQ FRAQ ERVASBEPRZRAGF 

TBYQ VF HAQRE SBEG XABK 

BAR VS OL YNAQ NAQ GJB VS OL FRN 

If the labels in column (2) are used, the machine express- 
es a Reverse Caesar Cipher. Here are some Reverse Caesar mes- 
sages for you to decipher: 

ULINFZ RH YVSRMW GSV KRXGFIV LU YRMXLOM 

YVDZIV GSV TILXVI SV RH Z IVW HKB 

ZOO RH OLHG UOW ULI BLFI ORUV 

You can compose your own secret code by scrambling the 
wires that run from switch 1 to switch 2. Make sure that one 
and only one wire runs from each of the 13 positions on switch 
1 to each of the 13 positions on switch 2. 

There are more than 6 billion different ways of connect- 
ing these switches; therefore you may be sure that if you mix 
the wires up well, no one will stumble on your manner of con- 
nection by chance. 



33 



Solutions to the Ciphers : (Caesar) 

WE ARE SURROUNDED SEND REINFORCEMENTS 

GOLD IS UNDER FORT KNOX 

ONE IF BY LAND AND TWO IF BY SEA 

(Reverse Caesar) 
FORMULA IS BEHIND THE PICTURE OF LINCOLN 
BEWARE TOE GROCER HE IS A RED SPY 
ALL IS LOST FLEE FOR YOUR LIFE 



34 - 



26. MACHINE TO PLAY NIM 

Problem . There are several ways of playing the game of 
Nim. One way is to set up four piles of matches, with the 
number of matches in each pile 4, 3, 2 and 1. The two players 
take turns. Each player must during his turn take one or more 
matches from any one pile (and may take the whole pile) . The 
player taking the last match wins the game. 

Here is a sample game: 

(1) the player going first takes 2 out of the first 

pile, leaving 2, 3, 2, 1; 

(2) the second player now takes 2 out of the second 

pile, leaving 2, 1, 2, 1; 

(3) the first player now takes 1 from the last pile, 

leaving 2, 1, 2, 0; 

(4) the second player now takes 2 from the first 

pile, leaving 0, 1, 2, 0; 

(5) the first player now takes 1 from the third pile, 

leaving 0, 1, 1, 0; 

(6) it is now clear that the second player loses, 

for whichever match he takes, the first player 
takes the other one and wins. 

The problem is to set up this variation of the game of 
Nim in a machine. The machine is to signal what move it makes 
in response to any position left by the human player. The four 
piles of matches are represented by four switches. Their pos- 
itions correspond to the number of matches left in the pile at 
any time. Switch A has positions and 1; Switch B has posi- 
tions 0, 1, 2; Switch C has positions 0, 1, 2, 3; and Switch 
D has positions 0, 1, 2, 3, 4. There is also a fifth switch, 
E, which has two positions, M, for Machine's Turn to Play, and 
P for Player's Turn to Play. 

The machine is to accept any move by the human player, 
and is to be able to signal unmistakably its own move. 

The machine is to play either first or second. If the 
machine plays first, it should always win; if the mach in e 
plays second, it should win if the player makes any mistakes. 



35 



The game is to start with the switches set in positions A 1, 
B 2, C 3, and D 4. 

How should the machine be designed? 

Solution , Following is a circuit for the machine: 



Switch D Switch C 

(2 Deck, (6 Deck, 

5 position) 4 position) 

•i o-, o 



Switch B Switch A 
(6 Deck, (2 Deck, 
3 position) 2 position) 




? 9^0 

Switch E 
(1 deck 
position) 



- 36 



To operate the machine, if it is the machine's move, set 
each switch at the position of the number of matches which is 
in the corresponding pile. Then turn the switch E to "Machine". 
If any one of the lamps A, B, C or D is lit, but the lamp E 
is not lit, turn the corresponding switch down (irrespective 
of whether other lights flicker on or off) until the lamp E 
lights. If any one of the lamps A, B, C or D is lit, and the 
lamp E is also lit, select the switch having the largest set- 
ting and turn it down by one. This is the machine's move. 

If it is the player's move, turn the switch E to "Player", 
and then turn down that one of the switches which gives effect 
to the player's move. 



27. MACHINE TO PLAY TIT-TAT-TOE 

Problem . The usual way to play tit-tat-toe is of course 
familiar to nearly everybody. The game is played on a criss- 
cross set of lines : • , 



and the two players enter naughts "0" and crosses "X" until 
one player gets three marks together in a straight line and 
thereby wins. If neither succeeds, the game is a draw. 

The problem is to set up a machine which will play tit- 
tat-toe with a human player, assuming that the machine plays 
first. 

Solution . Here is a solution. Let the squares of the 
board be numbered as follows: 



1 


2 


3 


8 


9 


4 


7 


6 


5 



There are three switches: 

1. Machine's Last Move: 2 decks, 10 positions 

2. Player's Current Move: a special three-deck swi tch 

(see the circuit diagram) with 10 positions and 
16 j umpers . 

3. Machine's Next Move: 2 decks, 10 positions 
There are two lights: 



37 - 



1. H, Machine Plays Here 

2. W, Machine Plays Here and Wins 
Following is the circuit diagram: 



Machine 's 
Last Move 
(Deck 1) 



f 
1 
L 

s 

3 ( 



Current 
Source 



Player's 

Current 

Move 



» CZjO 

^5 



□S 



6CZ39 < ?CD 



_S> czzj <2 £ 



^5> 



>ay 



o CD? <2_ 



otf 



Machine 's 
Next Move 
(Deckl) (Deck 2) 



_g^< 



H, Machine^ 
Plays 
Here 



14 Wipers 
in this 
deck 



» □ o- 



Machine 's 
Last Move 
(Deck 2) 



-o 

-o 



-OCZ3 I 

o 



W, Machine 
Plays Here 
and Wins 



All wipers are shown with the switch 
in the No. 1 position. Note the 
special arrangement of the wipers 
on the Player's Current Move Switch. 
All switches have positions "start" 
and 1 through 9. 



38 



The rules for playing with this machine are as follows: 

(a) The machine plays first; and all switches are 

turned to the start position. 

(b) Turn the Machine Next Move Switch until Lamp H 

lights 

(c) Then enter "X" on the board in the square indi- 

cated by the Machine Next Move Switch; and 
then set the Machine Last Move Switch at the 
same number as the Machine Next Move Switch. 

(d) Then you as the human player enter " 0" on the 

board in the square you choose, and turn the 
Player's Current Move Switch to indicate the 
square where you played. 

Repeat steps (b) through (d) until the game is over. 

If the lamp W lights, the machine plays where indicated, 
and wins. 

If the machine tries to play in a square already occupied, 
play in the opposite square instead (this happens on the last 
play when the game is already a tie) . 

Sample games produced by this machine are shown below; 



°1 


x 2 


03 


4 


X l 


x 4 


X 3 


°2 


X 5 



02 


*3 


4 


x 5 


X l 


°1 


X 4 


°3 


x 2 



01 


X2 


X4 




X l 


°3 


X 3 


°2 





02 


X3 




°3 


x l 


°1 




h 


x 2 



- 39 - 



28. TRANSLATOR FROM BINARY TO DECIMAL 

Problem , A kind of notation for numbers which is ver y 
widely used in automatic computers, "giant brains", is not 
decimal notation but binary notation . The first dozen numbers 
in binary notation are 0, 1, 10, 11, 100, 101, 110, 111, 1000, 
1001, 1010, 1011. Here the digits are only and 1, and the 
successive positions report powers of two. Starting at the 
right, the positions report 2 to the zero power or one, 2 to 
the first power or two f 2 to the second power or four, 2 to the 
third power or eight, etc. In this way, 1011 is one one, one 
two, no fours, and one eight, or a total of eleven. 

The reason why binary notation is very useful in automatic 
computers is that many devices for storing definitely and cal- 
culating rapidly are devices which have just two states: on or 
off; magnetized north-south or south-north; conducting or not 
conducting; etc. 

Furthermore, the addition and the multiplication table s 
in binary arithmetic are easy and simple, as follows: 



+ 


1 




1 


1 

1 10 



X 





1 











1 





1 



One of the operations needed is to translate from binary 
numbers to decimal numbers. 

What is a machine that will translate the binary numbers 
from to 1111 into decimal? 

Solution . The machine will have five switches: one each 
for the eightsdigit, the fours digit, the twos digit, and the 
ones digit; and a fifth switch for testing the decimal number 
which corresponds with the binary number. Following is the 
circuit. All the wipers are drawn in the zero position. 



- 40 



Binary Binary Binary Binary Decimal 
8's digit 4 f s digit 2 's digit 1 's digit Number 
Switch Switch Switch Switch Switch 




1=3 



15 
14 
13 
12 

11 
10 
9 
(3 
7 
6 
5 
4 

3 
2 

1 



"Correct Match" Light 

To operate this machine, first set up the binary number 
on the 4 binary dials. Then turn the decimal dial until the 
light is lit. The decimal dial indicates decimal equivalent. 



41 



29. TRANSLATOR FROM DECIMAL TO BINARY 

Problem . Another operation needed is translation from 
decimal notation to binary notation. What is a machine that 
will translate from decimal numbers to 15 to binary numbers 
from to 1111? 



Solution . This machine may be obtained by wiring a single 
switch with sixteen positions and five wipers, using the fol- 
lowing circuit. There will be four lamps, for the eights, 
fours, twos, and ones binary digits. When a lamp glows, i t 
indicates that the binary digit is 1; when the lamp is dark, 
it indicates that binary digit is zero. 



Following is the circuit: 



Source of Current 



a/ 



o- 

CHi 



t 



oa o 



3 o 

O-j 

o4 


o 

0-i i 

on 



oCD o 



fe 



(Wipers are shown 
with the switch 
in the zero po- 
sition; note 
particularly the 
wipers for fours 
digit lamp.) 



O ' Y Bin arv Digit Lamps 



to operate this machine, turn the switch to indicate the 
decimal number, and the corresponding binary number may be read 
in the lamps. Here lamp ON = 1, lamp 0FF=0. Note : This 
translator and previous one can be wired at the same time. 



42 



30. BINARY ADDING MACHINE 



Problem . Given two binary numbers, each of three digits. 
What is a machine which will give their sum, in binary? 

Solution . The input of this machine is six switches, 
three for the number A, and three for the number C. The binary 
digits are called successively the 4, 2, and 1 digits. Each 
of these switches has two positions, one for digit and one 
for the digit 1. 

The output of this machine is four lamps Lq, L4 , L2 , L 1 , 
corresponding to the 8, 4, 2, and 1 digits. When a lamp glows, 
it represents the digit 1; when it is dark, it represents the 
digit 0. Following is the circuit: 

Current Source o- 






34 



Li" 

6 o Q ' o 






o 0-+—0 1 






J" 

D 6 



00 o 6 



43 - 



31. BINARY MULTIPLYING MACHINE 

Problem . Given two binary numbers, each of two digits. 
What is a machine which will give their sum, in binary? 

Solution . The input of the machine will consist of four 
switches, A2 and Al for the number A and B2 and Bl for the 
number B. Each of these switches will have two positions, one 
for the digit and one for the digit 1. 

The output of this machine will consist of four lamps L8, 
L4 f L2, and LI, corresponding to the four digits in the 8, 4, 
2, and 1 columns, of the binary number, which is the product 
of A and B. When a lamp glows, it will represent the digit 1 ; 
when it is dark, it represents the digit 0. Following is the 
circuit: 



i 



x 



) <-»B 



© L 4 L 3 <$> L 1 (©^ 



♦ *■ 



A b ^L 



<n 



4 e 



44 



32. BINARY COMPARISON MACHINE 

Problem . If we use binary notation, we can within the 
limits of the same hardware compare two numbers that are larger 
than we can with decimal notation. 

Given two binary numbers each of three digits. What is 
a machine which will report whether A is greater than B t or A 
is equal to B t or A is less than B? 



Solution . The input of the machine will consist of six 
switches. Three of the switches will express the three digits, 
4, 2, 1 of the number A. The other three switches will express 
the three digits 4, 2, 1 of the number B. Each of these switches 
will have two positions, one for the digit and one for the 
digit 1. 



The 
G for "A greater 
less than B 



output of this machine will consist of three lamps, 
greater than B", E for "A equal to B", and L for "A 



Following is the circuit: 
Sourceo 



A4 



*2 



*-f"* « 1 B, 



©L 



<kl 



<® 



45 



33. "TWO-OUT-OF-FIVE" CODE TRANSLATOR 

Problem. In some computers and some telephone exchanges, 
there is an advantage in representing decimal digits by select- 
ing just two out of five possibilities (lamps, lines, relays, 
etc.), no more and no less. In this way if a unit of equipment 
fails, one or three possibilities will be selected, and an 
error signal can be at once produced. 

One of the "two out of five" codes which is widely used 
is the following: 







2 out of 


5 






2 out of 5 


Decimal 


Diqit 


Code 




Dec 


imal Diqit 
6 


Code 


1 


and 1 




2 and 4 


2 




and 2 






7 


and 7 


3 




1 and 2 






8 


1 and 7 


4 




and 4 






9 


2 and 7 


5 




1 and 4 









4 and 7 
(special) 



What is a machine that will give this code automatically? 

Solution . The input of this machine is one switch, with 
10 positions and two decks wired as shown in the follow i n g 
circuit. 



The output of this machine consists of five lamps bear- 
ing the labels 0, 1, 2, 4, 7. 

Current Source <> ~ 




7 Lamps 





Construction Kit No. 1 and Explanation of 


Them 


1. 


Parts List 


48 


2. 


Wire 


49 


3. 


Battery 


49 


4. 


Battery Clamp 


50 


5. 


Bulbs 


50 


6, 


Sockets 


50 


7. 


Nuts and Bolts 


50 


8. 


Screwdriver and Spintite 


50 


9. 


Cray off Pencil 


50 


10. 


On-Off Switch 


51 


11. 


Panel 


51 


12. 


Multiple Switches 


51 


13. 


Assembly of the Multiple Switches 


53 


14. 


Additional Material 


56 


15. 


Wiring Lists and Templates 


56 


16. 


Example 


57 


17. 


Detailed Wiring for "The Flashlight" 


59 


18. 


Detailed Wiring for "The Hall Light" 


60 


19. 


Detailed Wiring for "The Door Bell" 


61 


20. 


Detailed Wiring for "The Porch Light" 


61 


21. 


Detailed Wiring for "The Burglar Alarm" 


62 


22. 


Detailed Wiring for "The Two Jealous Wives" 


63 



47 



Part II : Materials in the Geniac Kit, 
and Explanation of Them 

The Geniac Electric Brain Construction Kit is a kit by 
means of which anyone can put together the machines of the types 
described in Part I (and many more besides) so that they will 
perform operations of reasoning and computing. 

The kit is harmless. It runs on one flashlight battery. 
Wires are connected by fastening them to the same nut and bolt 
and tightening the connection by gripping them between two 
bolts. No heat or soldering iron is required. DO NOT CONNECT 
this kit or any part of it to any home or industrial electrical 
power outlet: you are likely to destroy the material, and you 
may hurt yourself. 

The kit is simple, but nevertheless it takes effort and 
work to put the material together to make a functioning elec- 
tric brain. We urge you to take your time. If necessary, read 
the instructions several times. If the instructions are still 
not clear, read ahead and then return. 

1, Parts list . In Table 2-1 appears a list of the parts 
contained in the kit. (All figures over 20 are approximate.) 



Table 2-1 



50 feet Wire, insulated 
1 Battery, dry cell, flashlight, IJ2 volts 
1 Battery clamp 
10 Bulbs, flashlight, 1; 2 volts 
10 Sockets for flashlight bulbs 
90 Bolts, brass, 6/32 
180 Nuts, steel, 6/32 
Screwdriver 
Spintite 
Crayoff pencil 
On-Off Switch, assembled 
Panel, masonite, punched 
6 Multiple Switch Tops, circular, masonite, 

punched 
6 Bolts, steel, for center pivot 
12 Washers, steel 



48 



6 Washers, sponge rubber 
25 Jumpers, metal, brass plated 
1 Manual 

2. Wire . The kit gives you about 50 feet of wire cover- 
ed with insulation. This is like the wire which you will find 
connecting a lamp to a wall plug, or a telephone to the tele- 
phone box, but adapted for handling much smaller currents and 
voltages. Instead of two wires wound together, here is one wire 
only. In the wiring that you will need to do, your two wires 
will be taken care of when you make for yourself a complet e 
circuit, running from one end of the battery around some kind 
of loop to the other end of the battery. 

Your wire will need to be cut apart with a cutting pliers 
into lengths. Convenient lengths for the wire to be cut into 
are: 15 pieces about 6 inches long; 15 pieces about 12 inches 
long; and 15 pieces about 18 inches long. 

About three quarters of an inch of the insulation will 
need to be trimmed off at each end of each piece. You can trim 
this off neatly with a dull knife; you should try to avoid 
cutting or nicking the wire. 

Two remaining feet of wire should be stripped of insulation 
and cut into pieces 1% or L L 2 inches long. These pieces of bare 
wire will be used for making transfer contacts on the multiple 
switches, as will be explained later. 

3. Battery . This is an ordinary flashlight battery, of 
about one and a half volts. A volt is a unit of electric push, 
or electric pressure, or electric potential. All these terms 
mean the same thing. 

You can think of a battery as a pump, which is able to 
push electrons, or little marbles of electricity, away from the 
plus end of the battery and towards the minus end of the bat- 
tery, waiting for some kind of circuit at the minus end so that 
the electrons can flow around the circuit back to the plus end 
of the battery. A flow of electrons is an electric current . 

The filament in the bulb through which the electrons flow 
provides a resistance or restriction or narrowness for the flow 
of electrons, so narrow in fact that it heats up and glows with 
friction as the electrons go through it. 

If at some time your battery will not light a bulb, o r 

- 49 - 



will only make it glow feebly with a dim orange light, then 
your battery has run down. 

4. Battery Clamp . This consists of a mekal clip that 
fastens into the panel and which will grip your battery and 
hold it. You then can fasten connections to the battery clamp 
and yet snap out your battery when it is weak and snap in an- 
other stronger battery in place of it when you need to. 

5. Bulbs . You have ten small light bulbs in the kit. 
They will glow from a single flashlight battery. In order to 
make them light, you have to run one wire from the bottom metal 
plate of the battery to the side of the bulb, and another wire 
from the top of the flashlight battery to the center of the 
base of the bulb. Your connections must be clean, not oily, 
or corroded. 

Examine your bulbs closely from time to time and make sure 
that the filament, the little slender wire that you can see 
inside the glass bulb, is all in one piece. If it is broken, 
the bulb is spoiled. 

6. Sockets . You have ten sockets for flashlight bulbs. 
The sockets may be fastened to the frame pieces. They are for 
holding the light bulbs, so that they can be screwed in and out 
of their sockets. 

7. Nuts and Bolts . For fastenings, connections, and 
terminals, here and there all over the machine you have a sup- 
ply of bolts (90) and a supply of nuts (180). The bolts are 
of brass, the nuts are of steel, and they should give good 
electrical connections. A bolt is inserted through any hole; 
then a nut is screwed down tight on the bolt holding it in 
position; then the connecting wire is wound around the end of 
the bolt coming through; then a second nut is screwed down 
tight on the wire and the bolt so as to give a tight electri- 
cal contact. (For one or two of the machines you may need a 
few more nuts and bolts.) 

8. Screwdriver and Spintite . In order to fasten your 
nuts and bolts easily, you have a small screwdriver , which fits 
in the slot of the bolt and enables it to be turned, or aligned. 
You also have a small piece of hexagonal tubing (a spinti te ) 
which fits, over and grips the hexagonal bolt and enables it to 
be spun quickly down the shaft of the bolt, and tightened. 

9. Crayoff Pencil . For writing the names or letters 

- 50 - 



designating switches, switch-positions, and lights, you have 
a white "crayoff" pencil. This kind of pencil is made with a 
soap base formula, and the marks it makes can be wiped of f any 
surface with a wet cloth. Thus you can very easily change 
the labels from one experiment to the next. 

10. On-Off Switch . In the kit is a small assembled 
switch which is used for turning a machine on or off, and so 
we call it the on-off switch . This is the switch which enables 
you to put suspense and drama into your machine; for you set 
everything the way it should be, then talk about it and ex- 
plain it, and finally when you have your listener all keye d 
up and ready, you (or he) throws the switch that turns the ma- 
chine on. Then you both can see (if everything has been pre- 
pared correctly) that the machine behaves as it should. 

11. Panel . In order to assemble your materials together 
into a machine, you have a rectangular panel consisting of 
masonite (thin pressed f iberboard) . It contains holes for 
nuts and bolts so that the various parts of the set may be 
mounted together and assembled firmly. 

If you examine the panel, you will see two patterns of 
holes. One pattern (shown in Figure 2-1) consists of 102 holes 
arranged mainly in two rows through the middle of the panel 
from end to end. 



Figure 2-1 

In this set of holes, all the hardware of a machine is mounted 
except the "multiple switches", which will be explained in a 
moment. The second pattern consists of 6 rosettes of 65 holes 
in a circular arrangement (shown in Figure 2-2) . These are the 
6 "bases" of the multiple switches. 

12. Multiple Switches . The remaining material which you 
have in the kit consists of 6 round pieces of masonite, each 
containing 65 holes in the same circular arrangement (see Fig- 
ure 2-2) , and the hardware for assembling them into multi pie 
switches , switches which are able to switch many circuits at 
the same time. Each of the circular pieces of masonite is 



51 



about 4 3/8 inches in diameter, is illustrated in Figure 2-2, 
and is called a multiple switch top (or switch disc , or switch 
dial). 




In the panel each of the exactly similar sets of 65 holes 
is called a multiple switch base . In an early stage of the 
design of the kit, the switch bases were 6 separate pieces of 
masonite; but then it became evident that mounting of the hard- 
ware to make a machine would be better accomplished by having 
all the switch bases solidly connected. 

The top of a switch is fastened to the base of a switch 

by means of a center pivot , consisting of a long bolt, washers, 

and a sponge rubber washer; the assembly of the center pivot 
is shown in Figure 2-3. 

The holes (except the center hole) in each switch base 
and switch top are arranged in 4 rings and 16 spokes. The 
rings are called Ring 1, 2, 3, 4 going outward, and the spokes 
are called Spoke 0, 1, 2, 3 and so on around, to Spoke 15, 



52 - 



starting with the spoke directly to the right, and going 
counterclockwise. See Figure 2-2. 

Each of the holes in the switch base may or may not con- 
tain a brass bolt, called a t erminal , for making connections. 
The connections are made using two steel nuts, one for fasten- 
ing the bolt securely to the switch base, and the second for 
holding and tightening a wire around the bolt so as to make a 
good electrical connection with the bolt (see Figure 2-4) . 

Each pair of holes in a switch top, from Ring 1 to Ring 2 
or from Ring 3 to Ring 4 (or very rarely from Ring 2 to Ring 3) 
may or may not contain a .jumper (also called a wiper ) , a small 
piece of brass plated metal like a T fastener, as shown i n 
Figure 2-5. The two brass arms fit into holes in the switc h 
disc and are pressed down like a clasp. A jumper serves t o 
make and break electrical contact as the switch is turned. 

13. Assembly of the Multiple Switches . Before any o f 
the multiple switches can function, however, it must first be 
assembled. Into the base we have to insert a number of nut s 
and bolts to hold wire connections. Just where these are in- 
serted depends on the type of switch we desire to construct, 
two-position, or four-position, or some other type. 

Into the top of the switch we must insert a number of 
jumpers in order to make and break contacts. Each jumper is 
inserted along a spoke between one ring and the next. Just 
where the jumpers are inserted again depends on the type of 
switch we desire to construct. 

In order for the switch to stay in a position to which 
it is turned, the body of the jumper must line up with the 
slots in the heads of the bolts, and these slots must be in 
line with the spoke, and then the jumpers will have a tendency 
to catch in the slots of the screws, as they should, to hold 
the switch in position (see Figure 2-6) . Note that in Figures 
2-6 and 2-7 the rings and spokes are drawn as thin lines: 
these lines are not actually drawn on the switch discs nor the 
switch bases, nor do they represent electrical lines connecting 
terminals; instead they are drawn to make the layout clearer. 



- 53 






Pivot bolt 



Steel washer 
^ <r Switch top 



£ 



I 



Space 
I 



Switch base 



-Nut 



Sponge rubber washer 
Steel washer 



Figure 2-3 — Center Pivot Assembly 



Brass bolt 

Switch base >> 

Steel nut 



m^ 



Connector -** 



m 



<-Bare wire 



^•Second steel nut 



Ji 



Figure 2-4 — Assembly of Terminal Bolt and 
a Wire Connector 



Jumper arms 



Jumper arms bent down 



^ Jumper 
^body 
(a) Jumper, not mounted 



Switch 
~ top 



cr„ 



Jumper, inserted in two adjacent 
holes along a spoke 

(b) Jumper mounted in switch top 
Figure 2-5 — Jumper 



54 




Figure 2-6 —Slots c 
in heads of bolts 
lined up with the 
spoke 2> 




Figure 2-7 — Three Position Switch, Six 
Decks (or Poles or Levels) 

Now suppose we wanted to assemble a switch which would have 
any one of three positions A, B f and C t and which would be cap- 
able of switching every one of six different circuits, A way 
in which that switch could be assembled is shown in Figure 2- 
7, in which both the top and the bottom of the switch are drawn 
over each other. Six jumpers are inserted in the top of the 
switch, shown as 223 in Figure 2-7. It is important that jump- 
ers be inserted in pairs opposite each other, so that the top 
of the switch will stay parallel to the bottom of the switch. 
A total of six times six or 36 nuts and bolts are inserted in 
the bottom of the switch, in the spots marked* in Figure 2-7. 
They are in groups of six called decks (also called poles, or 
levels); these decks are electrically independent, and they 
enable us to switch 6 different circuits. The holes belonging 
in any one deck in Ring 1 or Ring 3 are connected together by 
wire, as shown by the heavy line; they are connected with one 
of the short wires Hi inches long. They are made electrically 



- 55 - 



common ; in other words, they are commoned . Together they con- 
stitute what is called a transfer contact . 

Let us now consider the layout of the spokes and the rings 
and the 64 holes which they produce. We can see that we c a n 
assemble a switch in a number of different ways. This is the 
advantage of the design of the multiple switch we have chosen 
(on which patent is being applied for). Here are the type s 
of switches that can be made with these parts: 





Maximum 


Number of Positions 


Number of Decks 


2 


16 


3 


10 


4 


8 


5 


6 


6 to 8 


4 


9 to 16 


2 



If nuts and bolts did not cost anything, we could insert 
64 nuts and bolts into the base of each switch and leave them 
there — ready for use in any switch. Actually, because the 
kit has a limited supply, it may be necessary to move nuts and 
bolts from one switch to another in order to make the different 
machines we want. 

In the case of jumpers, we shall fairly often have to move 
them to different places, in order to make different switches 
for different machines. 

14. Additional Material . You may obtain additional o r 
replacement material for this kit by buying it at a local store, 
or by writing to us. Obviously, if your battery runs down, 
or if you want more wire, or if you want more nuts and bolts, 
the easy thing to do is to buy them in your neighborhood. But 
for more switch disks or for more jumpers, etc., you will prob- 
ably need to write us. Prices for these items are listed on 
a price list which may be obtained on request. 

15. Wiring Lists and Templates . In work with electrical 
circuits we need to lay out beforehand what we are going to 
do. We need to design on paper how we are to connect the dif- 
ferent pieces of material. For this purpose, we use (1) cir- 
cuit diagrams, (2) wiring lists, and (3) templates. 

A circuit diagram , as mentioned before, shows the scheme 
of connection of batteries, switches, lights, etc., in order 



56 



to make the circuit. In a circuit diagram we pay little at- 
tention to the actual physical location of the material; w e 
just show a diagram of its arrangement. 

In a wiring list , we name the terminals, by words or let- 
ters or numbers, and we state, for every part of the circuit, 
what terminal is connected to what terminal. In a wiring list 
again we pay no attention to the actual spatial locations o f 
the terminals. 

In a template , the case is different; we show the wiring 
and for any difficult portions of the circuit, such as the mul- 
tiple switches, we show the approximate relative spatial loca- 
tion of the different pieces of material used in the circuit. 
In other words, we draw a picture of where the terminals are, 
and then we indicate the wiring either by drawing lines f o r 
the connections or by writing notes showing the connections. 

16. An Example . Suppose we have a circuit as shown i n 
Figure 2-8. This circuit consists of two switches A and B, 
each having the positions 1, 2, 3, two lights marked E and 0, 
and a battery. Only one deck of switch A is used but three 
decks of switch B are used. 



_b 



A- 1 



V i— J 



£-< 



y 1 

2 



3-2 



On-Off * Switch 



J 



Figure 2-8 — A Sample Circuit 



B-5' 



•f ■ 



fcH 



<$> o0 



What would the wiring list for this circuit be? It would 
be as follows: 



Wire From 



To 



1. One side of battery, Transfer of 

Battery Plus Switch A, Deck 1 



2. Switch A, Deck 1, 

output 1 

3. A-l, 2 • 



Transfer, Switch B, 
Deck 1 

B-2, T 



57 



Wire From To 

4. A-l, 3 B-3, T 

5. B-l, 1 One side of light E t 

E 1 

6. B-l, 2 One side of light O t 

1 

7. B-l, 3 B-l, 1 

8. B-2, 1 1 

9. B-2 f 2 El 

10. B-2, 3 B-2, 1 

11. B-3, 1 E 1 

12. B-3, 2 1 

13. B-3, 3 B-3, 1 

14. E 2 2 

15. E 2 One side of On-Off 

Switch 

16. Other side of Other side of battery, 

On-Off Switch Battery Minus 

Here then is an example of how a list of wiring instruc- 
tions for a circuit can be prepared. The list specifies where 
each wire comes from and where it goes. Furthermore, instead 
of running long wires from certain outputs of the decks of 
switch B over" to one side of the lights, we take short cuts by 
hitching on at an early point to a wire already running to the 
desired destination. 

Now some circuits are so simple that no wiring list is 
needed. In many complicated circuits (especially in circuits 
in computing machines and other kinds of large electric brains), 
the wiring is so complicated that a written-out wiring list is 
unavoidable. 

What would be the template for this circuit? 
- 58 - 



The way the template would look is shown in Figure 2-9, 
although here we have simplified the picture of the swi t c h 
base and the switch top so that we show only two rings instead 
of the four rings that it actually contains. We can see that 
there is a considerable difference between the circuit descrip- 
tion of a multiple switch and the template description of a 
multiple switch; but we can also see the close relation between 



them. 



Switch A 



Switch B 




Thick lines are wires; 
thin lines are not wires 



s\ 



$> 



On-Off 
Switch 



Light E Light 
Battery 

Figure 2-9 — Template for the Sample Circuit 



The question may be asked: Why in putting together the 
multiple switches, are jumpers, nuts and bolts inserted where 
they are not electrically necessary, as in Deck 2 of Switch A 
(in Figure 2-9) and in Deck 4 of Switch B? The answer is that 
the additional symmetrically placed hardware is needed for me- 
chanical reasons; by putting it in, the central rubber washer 
which acts as a spring will pull the switch top at right angles 
instead of obliquely, which would result in poor electrical 
contact. The mutiple switches should always be constructed 
symmetrically in this way for mechanical reasons. Since this 
mechanical aspect can from now on be deduced, we may omit this 
part of the assembly in the drawings of future templates. 

17. Detailed Wiring for "The Flashlight". We shall now 
consider the details of the assembling and wiring of the kit 
materials so as to make the first machine, "The Flashlight". 
Following is the template for this circuit : 



59 - 



Switch 




Light 



Battery 



Machine On-Off 
Switch 



One multiple switch only is needed. The top is fitted with 
two opposite jumpers. The base is fitted with eight bolts in 
the pattern shown. The battery is mounted on the panel in the 
battery clamp; the machine "on-off switch" is also mounted; 
and a light in its light socket is mounted. Wires run: from 
one side of the battery to a common terminal of Deck 1; from 
the "on position" of the switch to one side of the light (light 
socket); from the other side of the light socket to one side 
of the machine on-off switch; and from the other side of the 
machine on-off switch to the other side of the battery. 

18. Detailed Wirjftq for "The Hall Light" . Wiring list: 
From To 

1. Battery, Plus Upstairs Switch, Transfer 

2. Upstairs Switch, Position B Downstairs Switch, Position B 

3. Upstairs Switch, Position A Downstairs Switch, Position A 

4. Downstairs Switch, Transfer Hall Light, one side 

5. Hall Light, Other side On-Off Switch, one side 

6. On-Off Switch, Other side Battery, Minus 



- 60 



Template: 




Hall Light 



Battery 

19. Detailed Wiring for "The Doorbell" 
Front Door Back Door Side Door Garden Door 




Doorbell Ringing 

20. Detailed Wiring for "The Porch Light" 

H all Switch Upstairs Switch Attic Switch 




On-Off Switch 



61 - 



21. Detailed Wiring for "The Burglar Alarm" 




Window IWo 



Alarm Light 



62 - 



22 . Detailed Wiring for "The Two Jealous Wives" . Wiring 



To 
transfer, deck 1, switch Hi (Hl-1:T) 
transfer, deck 1, switch H2 (H2-1:T) 
safety light, side 1 
Wl-1: T 
W2-1: T 

safety light, side 1 

W2-2: T 
safety light 
Wl-2: T 

C-l: T 
C-2: T 
C-3: T 
C-4: T 
safety light, side 1 

danger light, side 1 

safety light, side 1 

danger light, side 1 

danger light, side 1 
safety light, side 1 
plus end of battery 
plus end of battery 



Instruct] 


ions: 


From 


Minus end of battery 


HI-, 


L: I 


H2- 


L: I 


H2-] 


L: N 


H2-2: I 


H2-2: N 


W1-] 


L: I 


Wl-j 


L: N 


W2-] 


L: I 


W2-1 


L: N 


W2-2: I 


W2-2: N 


Wl-2: I 


Wl-2: N 


C-l 


I 


C-l 


N 


C-L 


I 


C-2 


N 


C-3 


I 


C-3 


N 



C-4: I 

C-4: N 
danger light, side 2 
safety light, side 2 



In the above, T stands for "transfer contact"; I stands 
for contact "in canoe": N stands for contact "not in canoe". 



63 



T Y N I A C S®: 

TINY ELECTRIC BRAIN MACHINES, 
AND HOW TO MAKE THEM 



Si Also: 

Manual for Tyniac^ Electric Brain Construction Kit (K2) 



Edmund C. Berkeley 



Copyright 1956 by Berkeley Enterprises, Inc. 



Published, March 1956, by Berkeley Enterprises, Inc. 
513 Ave. of the Americas, New York 11, N. Y. 



Introduction 

This report and the accompanying kit present Tyniacs @ , 
tiny electric brain machines, M Tiny (TYNI) Almost -Automatic (A) 
Computers (CS)". They are electrical machines which are able to 
calculate and reason automatically although they are too small to per- 
form operations one after another automatically. They show, with 
the least hardware that we have yet been able to work out that still 
allows interesting experiments, the fascinating power and variety of 
computing and reasoning circuits. 

This set of thirteen experiments contains several puzzles, two 
game -playing machines, two arithmetical machines, and several rea- 
soning machines. Furthermore, at least fifteen of the experiments 
in our earlier and larger kit, our Geniac Electric Brain Construction 
Kit (Kl), can also be performed with the materials in this Tyniac 
Kit (K3). 

Each of the machines in these experiments uses one flashlight 
battery, not more than four flashlight lamps, and not more than four 
multiple switches. With the Tyniac kit, all connections are with nuts 
and bolts, and no soldering is required; the kit is completely safe. 
The kit, though inexpensive and convenient for constructing Tyniacs, 
is however not necessary; and some persons will prefer to construct 
their Tyniacs using other materials. 

We hope that you find this report and kit interesting, enter- 
taining and amusing, and that you will enjoy playing with the kit and 
entertaining your friends with the little machines that you make. 

If you find that at first you have some difficulty in understand- 
ing all that is in this report, TAKE YOUR TIME and think; make first 
the simpler machines; then try the more complicated ones. To make 
a machine that will reason and calculate you too must reason and cal- 
culate. 

Any comments, suggestions for new experiments, and correc- 
tions, will be gratefully received. We shall be glad to hear from 
you. 

8-145(P38 Edmund C. Berkeley 

- 2 - 



CONTENTS 



Page 



Part I: Tiny Electric Brain Machines 
Section 1: General Information 
Section 2: Circuits 
Section 3: Experiments 



1. Joe Savarelli's Rock Quarry 

2. Signals on the Mango Blossom Special 

3. General Alarm at the Fortress of Dreadeerie 

4. Ebenezer Graham's Garage Light 

5. The Game of Twenty -One in Sundorra 

6. The Two Suspicious Husbands at Great North 

Bay 

7. The Submarine Rescue Chamber Squalux 

8. Bruce Campbell's Will 

9. The Lock with 65,000 Combinations 

10. Sammy Buckley's Machine for Adding Dozens 

11. Johnny Greer's Machine for Checking 

Multiplication 

12. The Game of Black Match 

13. James McCarty's Logic 



Part II: Materials in the Tyniac Kit, and Explanation 
of Them 



Part III: Introduction to Boolean Algebra for Circuits 
and Switching 



- 3 



Part I: Tiny Electric Brain Machines 



Section I. General Information 

Question : What is an "electric brain machine"? 

Answer : An electric brain machine is a machine containing 
electric circuits which is able to calculate or reason automatically. 
The bigger electric brains are able to carry out long sequences of 
reasoning and calculating operations, thus solving complex problems. 
Such a machine is a true "electric brain machine", for there is no 
doubt that until such operations began to be done by machines, every- 
one agreed that such operations constituted thinking and were char- 
acteristically the operations carried out by brains. 

The first modern electric brain machine was finished at 
Harvard University in 1944, and has been working there ever since. 
Now thousands of such machines are in existence, and at work pro- 
ducing knowledge. This development is becoming so important that 
it is often called the "Second Industrial Revolution". 

Question : What is a TYNIAC? 

Answer : A TYNIAC is an electric brain machine which is 
tiny. If expense were no barrier, we could make one using only a 
small amount of hardware which would run extremely well doing 
many kinds of problems. But expense of course is a barrier, and 
the tiny electric brain machines which we talk about in this report 
are machines which are made of four multiple switches, a panel for 
mounting them, a flashlight battery, four flashlight bulbs, nuts, 
bolts, and other hardware. The tiny electric brain machines we 
talk about here will not run by themselves; that is, whenever the 
machine is supposed to do something, you yourself have to turn the 
switch representing the machine's action. ' But nevertheless these 
machines do calculate and reason automatically, because the way 
that they are wired expresses the calculating and the reasoning. 



- 4 - 



Question: What is the origin of the TYNIACS? 

Answer: In one sense all these little machines were created, 
(of course, usir>,g earlier ideas, suggestions, and research) in the five 
days December 27 to December 31, 1955, when they were designed for 
this kit. But in a larger sense of course, these little machines are the 
outgrowth of work which we have been doing for ten years, and which 
is still continuing — the exploration of intelligent behavior expressed 
in machines. For this purpose, we maintain a small laboratory, and 
are continually working on one phase or another of small robots and 
other machines which display intelligent behavior. Among other steps 
leading to the Tyniacs are the following. 

In 1950, for educational and lecturing purposes, we constructed 
a miniature electric brain called Simon. Although only 1-1/4 cubic feet 
in size, and limited in capacity, it was a complete automatic computer, 
and it could show how a machine could do long sequences of reasoning 
operations. The picture of Simon appeared on the front cover of two 
magazines, "Scientific American" and "Radio Electronics"; the mach- 
ine itself has been demonstrated in more than eight cities of the United 
States „ Over 350 sets of Simon plans have been sold. But this mach- 
ine costs over $300 for materials alone, and is therefore too expen- 
sive for many situations in playing and teaching. 

Soon after Simon was finished we began work to develop really 
inexpensive electric brains. By 1955, we had gathered and worked 
out descriptions of over 30 small electric brain machines, which 
could be made with very simple electrical equipment. These machines 
were incorporated in a construction kit, which would make any one of 
these little machines. The name of the kit was "Geniac Kit No. 1"; 
the word "Geniac" (g) came from the phrase "Genius Almost-Auto- 
matic Computer", and has been registered as a trademark. This kit 
made use of six multiple switches, and up to ten flashlight lamps and 
sockets, about twice as much hardware as the Tyniac kit contains. 
During 1955, we decided that a smaller, simpler, and better kit would 
be a good idea. This led to the Tyniac kit. 

Question: How am I to understand these experiments? 

Answer: The first thing to do is not to rush, but to take your 
time, and read as carefully as you can all the general information. 
Read particularly Section 2 of this part which talks about circuits and 
how they work. The circuits which make these machines operate are 

- 5 " 



all of them circuits in which electricity from a flashlight battery 
flows along wires and causes certain light bulbs to light up. The la- 
bels on the switches, on their positions, and on the lights show the 
meaning which is to be assigned 

In the same way, in the pilot's cabin of an airplane, or on the 
operating panel of an oil refinery, the switches, the lights, the dials, 
and the labels tell the meaning of what is going on, so that the air- 
plane or the refinery can be controlled. 

Question: How are circuits like those in the experiments designed? 
I notice that each experiment is set up as a problem and solution: 
how would I be able to work out the solution for myself? 

Answer : This is an interesting and important subject, the 
design of switching circuits. If you find the subject really interest- 
ing and worth a lot of work, and want to do that work, then you are 
likely to be well qualified to be an electrical engineer or electronic 
engineer, or a designer of computing machines, and you may have an 
excellent professional future lying in front of you. 

An introduction to the design of switching circuits is given in 
Part m of this manual, using one of the best approaches, a new kind 
of algebra called Boolean algebra. This is the algebra of AND, OR, 
NOT, EXCEPT, UNLESS, IF. .. THEN, IF AND ONLY IF, and some 
other very common words and expressions of language and logic. 
This algebra is a part of the subject called symbolic logic, and has 
an important application to any circuits that make use of circuit ele- 
ments that can be either on or off, lighted or not lighted, conducting 
or not conducting, and so forth. 

Section 2. Circuits 

The tiny electric brain machines described in this report are 
made of: a battery, or source of electric current; wires, which con- 
duct it; switches, which change the paths along which the current 
flows; lights, which show where the current is flowing; and other 
hardware, such as nuts and bolts, which enables the whole machine 
to function together. In all of these machines the current starts from 
one end of the battery and flows in a path or circuit that eventually 
returns to the other side of the battery. 

Circuit Diagram. The diagram of the circuit or circuit diagram 
or circuit schematic shows the scheme of connection of the battery, the 
switches, and the lamps, in order that the machine will function as it 
is supposed to. The diagram does not necessarily show the physical 



Fig. 1 . - Battery 



Source 



Ground 



Fig. 2 - Battery terminals, 
when separated 



j 



Fig. 3 - Wire, or conductor 



J — f 



Fig. 4 - Electrical connections 



Fig. 5 - No electric connection 



<D 



Fig. 6 - Lamp bulb 



/Contact 



, -Contact 
Fig. 7 - A Switch 



Hinge 



_J,Hin 



Contacts 



ge 



Contadts 
Fig. 8 - Two-Position Switch 
(two ways of drawing 
it) 



I 



Hinge 



# Contacts 
Fig. 9 - Three -Position Switch 



Hinge 

.Contacts 
Fig. 10 - Four-Position Switch 



location of the hardware but only' the arrangement of the connections 
of the hardware. 

The symbols used in our circuit diagrams are sh own in the 
accompanying figures. We need to pay attention only to a few kinds of 
hardware. 

Battery. Fig. 1 is the diagram for a battery. The long and 
short lines supposedly represent the two kinds of plates in a battery 
by means of which the electric current is generated. The number of 
long and short lines does not symbolize anything, and does not have 
a special meaning. 

Instead of showing the two ends of the battery located next to 
each other, another method may be used (see Fig. 2) . One end or 
pole of the battery may be shown at one place as a small letter "o" 
meaning "source of current". The other end or pole of the battery 
may be shown at another place with the symbol "J_" meaning the 
"sink of current" or "ground". 

Wire. A line in a circuit diagram (see Fig. 3) represents an 
insulated wire, a connector from some point to some other point. 

Dots (see Fig. 4) represent points where electrical connec- 
tions are established by fastening two wires together so current can 
flow easily between them. 

In Fig. 5, two wires cross (drawn in either one of two ways) 
but there is no electrical connection between them. One wire is ac- 
tually either above or below the other. 

Lamps . The diagram of Fig. 6 sketches the glass bulb and 
the filament of the lamp. The two dots are its connections. 

Switches. A switch was originally a device for shifting a train 
from one track to another. Now in addition, it is a device for turning 
an electric current from one path to another; see Fig. 7. 

In Fig. 8, 9, and 10, appear more abbreviated diagrams of 
switches; they are diagrams therefore easier to draw. 

Switch Contacts. In any switch, the contacts have names. 
See Fig. 11 for examples of switch contacts and their possible names. 



- 8 



Transfer 
Contact 



Transfer 



Normally^ 

Closed 

Contact 



Normally! 

Open 

Contact 



• • • 

A B C 



Figure 11 — Contacts, and their Possible Names 

T-l T-2 T-3 T-4 

Z-l / Z-2 / Z-3/ 

/■: /. /. / 

A-l B-l C-l A-2 B-2 C-2 A-3 B-3 C-3 A-4 B-4 C-4 
Figure 12 — Four -Deck Three -Position Switch 



(Deck Z-3) 




A^4 (Deck Z-4) 
Figure 13 — Four- Deck Three-Position Switch Z 



- 9 



Decks. A single switch may be constructed having two or 
three or more electrically nonconnecting sections (often called decks 
or poles ) so that as it is turned, it simultaneously switches two or 
three or more electrically independent paths. In circuit diagrams 
this property of a switch may be shown by using a name for the switch 
and numbers 1, 2, 3, etc. , for the decks. For example, a switch 
(named Z) with three positions (A, B, and C) and four decks (named 
1, 2, 3, and 4) is diagrammed in Figure 12. 

Suppose however we actually wanted to make such a switch; 
it should have three positions and should enable us at one and the same 
time to shift four separate circuits. We could make it as shown in 
Figure 13. We could start with a flat round piece of non-conducting 
material. We could fasten jumping or bridging conductors along four 
radii in such a way that when we turn the switch at its central hinge 
or pivot, each jumper (drawn as GZ3)is shifted simultaneously and 
transfers current from its transfer points T to its corresponding con- 
tact points A, B, C. This idea is at the heart of the multiple switch 
used in the Tyniac kit (and also the Geniac kit). Examine the round 
discs in the kit. Each has a pattern of 65 holes, a center hole for a 
hinge or pivot, and four rings of holes arranged along 16 spokes (or 
radii). With the hardware in the kit, we can assemble these discs to 
switch many different circuits; see Part 2 of this manual for the de- 
tails. 

With these preliminaries out of the way, let us consider the 
first machine. 



10 



Pa rt I. Section 3 . EXPERIMENTS 

1. Joe Savarelli's Rock Quarry 

Problem: Joe Savarelli has a rock quarry where he takes out rock, 
puts it through his rod crusher, and makes crushed rock and gravel 
to put on roads. He drills holes in the bedrock of the quarry walls, 
puts in dynamite sticks, and explodes them electrically. 

What is the circuit for setting off the dynamite? 

Solution : Far enough away from the rock to be exploded, Joe 
sets a switch. The switch has two positions "Safe" and "Explosion". 
Next to the switch he sets a battery, and gets ready to connect one 
side of the battery to the Transfer Contact on the switch. Then he in- 
serts a detonating cap with the dynamite in the hole drilled in the 
rock, and runs a pair of wires from the detonating cap to the switch 
and to the battery. (See the circuit below. ) When he closes the 
switch at a distance, the detonating cap explodes and sets off the 
dynamite (shown by the lighting of the lamp "Dynamite Explodes"). 

Following is the circuit: 




Transfer 
Contact „ >%E3# Saie 



Dynamite 
Explodes 



\. Switch 

Figure 14 

Comments : This is an example of one of the simplest possible 
circuits: one switch with two positions that either turns off or turns 
on a light. The same circuit essentially turns off or turns on any 
room light, any lamp light, any flashlight, etc. 



11 



2. Signals on the Mango Blossom Special 

Problem: The Mango Blossom Special, a lcng streamliner, 
has four passenger conductors, Anderson, Bothwick, Cohen, and 
Davis. Many of , the stations along the railroad have curved platforms; 
also sometimes they are foggy, since the railroad is near the sea- 
coast; so the conductors often cannot signal using lanterns. There- 
fore, each conductor in his section of the train has a switch to signal 
the engineer's cabin, that all passengers in his section have finished 
leaving and boarding, and, so far as he observes, it is safe to pro- 
ceed. In the engineer's cabin, there is a panel light which shines 
only after all of the conductors have signaled "Go On": 

What should the circuit be? 

Solution : There will be four switches, named according to 
each conductor: "Anderson, Bothwick, Cohen, Davis". Each will 
have two positions, "Wait 1 * and "Go On". There will be one output 
light. Following is the circuit: 




Davis 



I Engineer's 
Panel 
Light Figure 15 



Comments : This circuit is a sample of what is called a 
series circuit . Only when all of the switches are turned on is the 
circuit closed. 



- 12 



3. General Alarm at the Fortress of Dreadeerie 

Problem: In the heart of the Inaccessible Mountains is lo- 
cated the Fortress of Dreadeerie inhabited by the Singular Dwarfs. 
They mine uranium; and they are fearful of invasion and conquest 
from any one of four types of dangers. First, there are the Elves of 
Kalkain; they are invisible, but they can be detected because they trip 
the infrared detectors. Second are the Gnomes of Minx; they also are 
invisible, but can be sensed by ultrasonic detectors. Third, there 
are the Leprechauns of Freemark; they are also invisible and travel 
with great speed; but they can be detected by radar because they re- 
flect radar pulses. Finally, there are the Trolls of Southway; they 
are also invisible, but they can be detected by ultraviolet detectors. 
The dwarfs desire a general battle alarm just as soon as any one of 
their four types of detectors reveals the approach of any of these 
dangers. 

What should the circuit be? 

Solution : There will be four switches: Infrared Detectors, 
Ultrasonic Detectors, Radar Detectors, and Ultraviolet Detectors. 
Each switch will have two positions: Safe, and Danger. There will 
be one output light: General Battle Alarm. Following is the circuit: 




Radar Detector^______lJltraviolet Detector. 

General 
Battery M ,|,^ (£> 3^ Flgure 16 



Comments : This is a sample of a kind of circuit called a parallel 
circuit . When any one of the switches is turned on, then the lamp in 
the circuit lights. 



4. Ebenezer Graham's Garage Light 

Problem: Ebenezer Graham has a light over the entrance to 
his garage, which illuminates his whole yard and enables him to see 
who is out there. There are four places where he wants to have 
switches, so that moving any switch either way turns the light on if 
it was off and turns the light off if it was on. These places are the 
front hall, Graham's own bedroom upstairs, the porch, and the 
garage itself. 

Set up a circuit which will accomplish this. 



Solution: There will be four switches: M Hall Switch, Bedroom 
Switch, Porch Switch, Garage Switch". Each will have two positions, 
which we may call A and B. There will be one output light, the 
'^Garage Light". The circuit appears in Figure 17. 

Note : If a switch has more than one jumper, we need to have a 
pointer (drawn as]>>, over a certain one of the jumpers xzzBl) to 
show at what position the switch is set. Even if a switch has only one 
jumper, it may be helpful to draw the pointer. 



Source 




Porch Switch 



14 - 



5. The Game of Twenty -One in Sundorra 

Problem: In the little principality of Sundorra, where the Pyre- 
nees Mountains meet the Caspian Sea, a form of the game of Twenty- 
One is often played. 

There are two players who each take turns. Each turn consists 
of two moves: the first move is the rolling of a die, which will come 
up, of course, with 1 to 6; the second move consists of choosing a 
number 1, 2, 3, or 4. The total of points by both players is con- 
tinually accumulated. The player who makes the accumulated total 
score nearest to but not exceeding 21 wins the game. If he makes 
the total go over 21, he loses the game. At his last turn, if the roll 
of the die makes the total exactly 21, the player does not have to take 
his second move; but at all previous turns, he does have to. 

For example, here is a game between Bill and Ed: 

Move No. Turn Source of Move Points Total Points 



1 


Bill 


Die 


3 


3 


2 


ii 


Choice 


1 


4 


3 


Ed 


Die 


2 


6 


4 


ti 


Choice 


4 


10 


5 


Bill 


Die 


6 


16 


6 


it 


Choice 


4 


20 


7 


Ed 


Die 


3 


23 



Therefore Bill wins, because his last move left 20 as the qualifying 
total. 

The Syndicate at Sundorra, finding out that the game is a great 
attraction, orders a number of machines that will play the game with 
human players. 

What is a strategy for these machines, and a circuit by means 
of which the machine can make its moves? 

Solution: The strategy for the machine depends only on the 
accumulated total score at the time that it moves. A reasonable 
strategy is expressed in the following table, which is built into the 
wiring of the circuit shown in Figure 18. 



- 15 - 



Total Score 


Machine T s Move 


1, 14 


4 


2, 15 


4 


3, 16 


4 


4, 17 


4 


5, 18 


3 


6, 19 


2 


7, 20 


1 


8 


1 


9 


1 


10 


1 


11 


1 


12 


4 


13 


4 



There will be one switch, the "Total Score Switch", with po- 
sitions as shown in the "Total Score" of the table above. There will 
be four output lights showing the "Machine's Move", 1, 2, 3, or 4. 
Following is the circuit: 




Total Score Switch 



Lights 

12 3 4 

Machine T s Move — 

Ground 



Figure 18 



16 



6. The Two Suspicious Husbands at Great North Bay 

Problem : One summer two couples vacation in nearby cottages 
on the shore of Great North Bay. The two husbands, George and 
Harry, are suspicious, and one day agree that the wife of either one 
(Violet or Winifred, respectively) may not go boating alone with the 
other husband. They are handy with electric circuits and they set 
up a wiring system in the boathouse; they arrange with the boat boy 
to turn switches to show who is out in the boat. In each of their own 
cottages they install a danger light to shine when the situation is 
contrary to their agreement, and a safety light to shine on other 
occasions. 

How should the circuit be wired? 

Solution : There will be four two-position switches marked 
"George, Harry, Violet, Winifred". One position stands for "in the 
boat". The other position stands for "not in the boat". There will 
be two lights "Danger, Safety". Following is the circuit: 



Source 



In the boat 




Violet 



Figure 19 



- 17 



7. The Submarine Rescue Chamber Squalux 
Problem : The submarine rescue chamber Squalux has: 

— a Main Door for passage to and from the mother 

ship (the Luxor), when the Squalux is properly 
connected; 

— a Bottom Door for use when the rescue chamber 

has been lowered through the water and fastened 
on top of a crippled submarine, to be used for 
passage through the submarine hatch; 

— an Emergency Door, for use in case of accident, 

allowing some one inside the Squalux to enter 
the ocean and try to swim to the surface; 

— an Air Pump, which pumps air into the Squalux 

until it reaches the ocean depth pressure; 

— an Air Valve which lets air out of the Squalux 

until it reaches sea level pressure. 

The rules are these: (1) you should be able to open the Bottom 
Door only when the Squalux air pressure equals the ocean depth 
pressure, the Squalux is properly connected to the crippled submar- 
ine, the air valve is closed, and the air pump is off; (2) you should 
be able to open the Main Door only when the Squalux air pressure is 
at sea level, the Squalux is properly connected to the Luxor, the 
pump is off, and the valve is closed; (3) you should be able to open 
the Emergency Door when the Squalux air pressure is at minimum 
safe pressure, irrespective of the pump and valve condition, and 
connections. 

How should the circuit be wired? 

Solution: There will be four switches: "Connection, Pressure 
Gage, Pump, Valve". The Connection switch will have two positions: 
"Complete to the Crippled Submarine", "Complete to the Mother 
Ship Luxor". The Pressure Gage switch will have three positions: 
"Ocean Depth Pressure, Minimum Safe Pressure, Sea Level Pres- 
sure". The Pump switch will have two positions: "On, Off". The 
Valve switch will have two positions: "Open, Closed". There will 

- 18 - 



be three output lights: "Light 1, Safe to Open Main Door; Light 2, 
Safe to Open Bottom Door; Light 3, Safe to Open Emergency Door". 
Following is the circuit: 



Ocean Depth Pressure 




Light 1 Light 2 

Safe to Safe to 

Open Main Open 



Light 3 
Safe to 
Open 



1 



r=r Ground 



Door 



Bottom Door Emergency Door 



Figure 20 



19 



8. Bruce Campbell's Will 

Problem: Bruce Campbell, a relative of the old Scotchman 
Douglas Macdonald, was rather impressed with his kinsman's will, 
and decided to model his own will somewhat after it. This was Bruce 
Campbell's will: 

If at my death my son, Bruce Campbell II, is not living, and if 
no son of his and grandson of mine bearing the name Bruce Campbell 
HI, is then living, then 40% of my estate will be paid to the heirs of 
my son. If my son is living at my death, and is not a graduate of 
Edinburgh University and is not married, and has no son named Bruce 
Campbell in, then 40% of my estate will be paid to my son. If my son 
is living, but is a graduate of Edinburgh University or is married, 
but has no son named Bruce Campbell in, then 60% of my estate will 
be paid to my son. If my son is living and has a son named Bruce 
Campbell HI, then my son will get all of my estate if he is a graduate 
of Edinburgh University but only 80% of my estate if he is not a gradu- 
ate. If my son is not living but if he had a son named Bruce Campbell 
III who is living at my death, then 80% of my estate will be paid to 
Bruce Campbell in or his legal guardian. Any balance of my estate 
wiU be paid to the Gaelic Home for the Aged and Indigent. 

How much of Bruce Campbell's estate is paid to his son or his 
son's heirs? What is a circuit which will show quickly what is paid? 

Solution : There will be four switches each with two positions: 
Son Living or Not; Son a Graduate or Not; Son Married or Not; and 
Grandson Named Bruce Campbell in Living or Not. There will be 
four output lights: 40%, 60%, 80%, and 100% showing the proportion of 
Bruce CampbeU's estate payable to Bruce Campbell II or his heirs. 
Following is the circuit: 



- 20 



Source 



Yes 



Son Bruce Campbell II 
Living or/ Not 




40% • 60% 80% 100% 



Ground 



Figure 21 



21 



9. The Lock With 65, 000 Combinations 



Problem: • Make a combination lock which will become "unlocked" 
only when each one of four switches is set at a particular one of the 
sixteen letters A to P. For example, choose as the first combination 
for the lock the combination G J C P. 



Solution : There will be four switches each with one deck and 
sixteen positions. The switch names will be "First Letter, Second 
Letter, Third Letter, Fourth Letter. " The sixteen positions will be 
the letters A to P inclusive. There will be one output light, "Unlock- 
ed. " Following is the circuit: 
Source 




Second Letter 



Unlocked" 
Light 



Ground 



Third Letter 



Fourth Letter 



Figure 22 



Notes : 1. Clearly, any other four-letter combination (with 
letters not beyond P) can be easily and quickly set on the switches 
by changing one of the two connections of each one of four wires. 
2. The actual number of the possible combinations is 16 times 16 
times 16 times 16, or 65, 536. 



22 



10. Sammy Buckley's Machine for Adding Dozens 

Problem: Sammy Buckley is having trouble remembering the 
results of adding dozens, such as 36 and 48. So he decides to make 
himself a machine for checking the results. One switch is the 1st 
Number to be Added, which may be positioned at 24, 36, 48, or 60. 
The second switch is the 2nd Number to be Added, which may be 
positioned at any one of the same numbers. The third switch is the 
Sum, which may be positioned at any of the numbers 48, 60, 72, 84 
96, 108, 120. There is one output light which shines only when the 
answer is correct. 

What should the circuit be? 

Solution : Following is the circuit. 

Note . In this case, to simplify the wiring between the second 
switch and the third switch, each wire leaving the second switch is 
marked with a "tag" telling to what terminal it goes on the third 
switch. This method saves cluttering up the circuit diagram with 
very many lines. 



To 72, 



To 84 



To 60 



d^) P 2°4 9, To 48 
To 120 




To 72 



To 108 
To 96 



Switch: Second Number 
to be Added 



"Correct" 
Ground 



Sum Switch 



Figure 23 



23 



11. Johnny Greer's Machine for Checking Multiplication 

Problem: Johnny Greer has trouble remembering the six, seven, 
eight, and nine times multiplication tables. So he decides to make 
himself a machine for checking the results. One switch, the Multi- 
plicand, may be set at 6, 7, 8, or 9. The second switch, the Multi- 
plier, may be set at 6, 7, 8 or 9. The third switch, the Product, 
may be set at any of the ten numbers 36, 42, 48, 49, 54, 56, 63, 64, 
72 and 81. There is one output light which shines when the answer is 
correct. 

What should the circuit be? 

Solution : .Following is the circuit: 



Source 




Multiplicand Switch 




To 49 To 42 To 54 

To 48 

To 42 
To 36 

To 81 
To 72 
To72 To'54 To63 
Multiplier Switch 



"Correct" 
Light 



Product Switch 



Ground — 



Figure 24 



- 24 



12. The Game of Black" Match 

Problem: In the game of Black Match, two players start with 
22, 23, 24, or 25 matches, one of which is black. Either player 
may take 1, 2, 3, or 4 matches, when it is his turn, and he must 
take at least one match. The object of each player is to compel the 
other player to take the Black Match, the last match. 

For example, here is a typical game, begun with 23 matches. 
The machine has the first move, and takes 2 matches. The player 
now takes one match. The machine takes 4 matches. The player 
takes 3 matches. The machine takes 2 matches. The player takes 
2 matches. The machine takes 3 matches. There are now left 6 
matches. The player takes 4 matches; the machine then takes one 
match; and the player is left with the last match, the Black Match, 
which he has to take, and loses. 

Set up this game in a machine so that a human player can play 
the game with the machine; the machine is to have the first move, 
and the machine is to win all the time. 

Solution: There will be three switches. The first switch is the 
Starting Number Switch, which has four positions 22, 23, 24, and 
25 according to the number of matches with which the game is started. 
The second switch is the Machine's First Move Switch, with two 
positions: First Move, and Not the First Move. The third switch is 
the Player f s Current Move Switch. The four output lights show, 
after each move by the human player, the number of matches 1, 2, 
3, or 4 that the machine takes at its next move. 



- 25 - 



Source 




-=- Ground 
Starting Number Switch Number of Matches Machine Takes 



Figure 25 



- 26 



13. James McCarty 's Logic 

Problem: James McCarty, Prime Minister of Adventularia, 
in his public speeches reasons as follows: 

All Theodosians attack me. 

General Valorous attacks me. 

Therefore, General Valorous is a Theodosian. 

A professor in one of the colleges of Adventularia constructs a mach- 
ine for handling this and similar kinds of reasoning, a machine called 
a syllogism machine. 

How should it be designed? 

Solution : A syllogism machine that will handle this kind of rea- 
soning is as shown in Figure 26. In McCarty's argument, the a T s 
are Theodosians, the b's are those who attack McCarty, and the c's 
are General Valorous all by himself. 



1st Premise (No Switch Required): All a's are b's 
Source ^ jo 1 



To 3 
To 2 / 




2nd Premise 



To 2 
ftll c's are b's 
All c's are a's 

All b's are c's 
(C ^f All a's are c's 

^•To 3 
To 2 



Light 
3 



2 ally Logically Trivial^ 



Logically Logically 

Valid Not , but -zHround 

Valid Logically -° rouna 

Valid 



Figure 26 

- 27 - 



Part II: Materials in the Tyniac Kit, 

and Explanation of Them 

With the Tyniac Electric Brain Construction Kit anyone can put 
together the machines of the types described in Part I (and many 
more besides), so that they will-perform operations of reasoning 
and computing. 

The kit is harmless.. It runs on one flashlight battery. Wires 
are connected by fastening them to the same nut and bolt and tighten- 
ing the connection by gripping them between two bolts. No heat or 
soldering iron is required. DO NOT CONNECT this kit or any part 
of it to any home or industrial electrical power outlet; you are likely 
to destroy the material, and you may hurt yourself. 

The kit is simple, but nevertheless it takes effort and work to 
put the material together to make a functioning electric brain. We 
urge you to take your time. If necessary, read the instructions 
several times. If the instructions are still not clear, read ahead 
and then return. 

1. Parts List. In the following table appears a list of the parts 
contained in the kit. (Figures over 20 are approximate.) 

TABLE OF PARTS 

See 
No. Item Paragraph 

1 Coil of 25 feet of insulated wire 2 

1 Battery, dry cell, flashlight, 1 1/2 volts 3 

1 Battery clamp 4 

4 Bulbs, flashlight, 1 1/2 volts 5 

4 Sockets for flashlight bulbs 6 

60 Short bolts, 6/32, 1/2 inch long 7 

140 Hexagonal nuts, 6/32, 1/4 inch diameter 7 

1 Spintite blade 8 

1 Panel, masonite, punched 9 

4 Multiple Switch Discs, circular, 10, 13 

masonite, punched 

14 Long bolts, 6/32, 7/8 inch, for 10 
center pivot, etc. 

16 Washers, hard 10 

4 Washers, sponge rubber 10 



28 



See 
No. Item Paragraph 

8 Jumpers, metal, brass 11 

36 Wipers, phosphor bronze 12 

1 Manual 

1 Set of Labels 15 

1 Set of Templates 16 

Each of these items will now be described. 

2. Wire . The kit provides about 30 feet of wire covered with 
insulation. This is like the wire which you will find connecting a 
lamp to a wall plug, or a telephone to u:.e telephone box, but adapted 
for handling much smaller currents and voltages. Instead of two 
wires wound together, here is one wire only. In the wiring that you 
will need to do, your two wires will be taken care of when you make 
for yourself a complete circuit, running from one end of the battery 
around some kind of loop to the other end of the battery. 

Your wire will need to be cut apart with a cutting pliers into 
lengths. A convenient length for most of the wire to be cut into is 
14 inches, but some pieces can be shorter, about 8 inches long. 

About three quarters of an inch of the insulation will need to be 
trimmed off at each end of each piece. You can trim this off neatly 
with a dull knife; you should try to avoid cutting or nicking the wire 
since this will shorten the length of time it will last. 

A small amount of the wire should be stripped of insulation and 
cut into pieces 1 or 2 inches long. These pieces of bare wire will be 
used for making transfer contacts on the multiple switches, as will 
be explained later. 

3. Battery. This is an ordinary flashlight battery, of about one 
and a half volts. A volt is a unit of electric push, or electric pres- 
sure, or electric potential. All these terms mean the same thing. 

You can think of a battery as a pump, which is able to push elec- 
trons, or little marbles of electricity, away from the plus end of the 
battery and towards the minus end of the battery, waiting for some 
kind of circuit at the minus end so that the electrons can flow around 
the circuit back to the plus end of the battery. A flow of electrons is 
an electric current. 



29 



The filament in the bulb through which the electrons flow provides 
a resistance or restriction or narrowness for the flow of electrons, 
so narrow in fact that it heats up and glows with friction as the elec- 
trons go through ito 

If at some time your battery will not light a bulb, or will only 
make it glow feebly with a dim orange light, then your battery has run 
down, and should be replaced. 

4. Battery Clamp . This consists of a metal clip that is fastened 
with nuts and bolts into the panel and which will grip your battery and 
hold it. You then can fasten connections to the battery clamp and yet 
snap out your battery when it is weak and snap in another stronger 
battery in place of it when you need to. 

5. Bulbs. You have four small flashlight bulbs in the kit. They 
will glow from a single flashlight battery. In order to make them 
light, you have to run one wire from the bottom metal plate of the 
battery to the side of the bulb, and another wire from the top of the 
flashlight battery to the center of the base of the bulb. Your connec- 
tions must be clean, not oily, or corroded. 

Examine your bulbs closely from time to time and make sure 
that the filament, the little slender wire that you can see inside the 
glass bulb, is all in one piece. If it is broken, the bulb is spoiled. 

6. Sockets. You have four sockets for flashlight bulbs. The 
sockets may be fastened to the panel. They are for holding the light 
bulbs, so that they can be screwed in and out of their sockets. 

7. Nuts and Bolts . For fastenings, connections, and terminals, 
here and there all over the machine, you have a supply of bolts and a 
supply of nuts. The nuts and bolts are of cadmium -plated steel, and 
give good electrical connections. A bolt is inserted through any hole; 
then a nut is screwed down tight on the bolt holding it in position; 
then the connecting wire is wound around the end of the bolt coming 
through; fhen a second nut is screwed down tight on the wire and the 
bolt so as to give a tight electrical contact. 

8. Spintite Blade. In order to fasten your nuts and bolts easily, 
you will need a small screwdriver, which will fit in the slot of the 
bolt and enable it to be turned. You also have in the kit a small piece 
of hexagonal tubing (a spintite blade) which fits over and grips the 



30 



hexagonal bolt and enables it to be spun quickly down the shaft of the 
bolt, and tightened, with the screwdriver holding the bolt. 

9. Panel. In order to assemble your materials together into a 
machine, you have a rectangular panel consisting of masonite (thin 
pressed fiberboard). It contains holes for nuts and bolts so that the 
various parts of the set may be mounted together and assembled 
firmly. 

If you examine the panel, you will see two patterns of holes. 
One pattern (see Figure 2-1) consists of 68 holes arranged in sev- 
eral rows through the middle of the panel from end to end. 



Figure 2-1 



In this set of holes, all the hardware of a Tyniac machine is mounted 
except the "multiple switches' 1 , which will be explained in a moment. 
The second pattern consists of four rosettes of 65 holes in a circular 
arrangement (see Figure 2-2). These are the four "bases" of the 
multiple switches. 

10. Multiple Switches. The remaining material provided in the 
kit consists of 4 round pieces of masonite, each containing 65 holes 
in the same circular arrangement (see Figure 2-2), and the hard- 
ware for assembling them into multiple switches, switches which are 
able to switch many circuits at the same time. Each of the circular 
pieces of masonite is about 4 3/8 inches in diameter, is illustrated 
in Figure 2-2, and is called a multiple switch top, or switch disc , 
or switch dial, or simply a disc. 

In the panel each of the exactly similar sets of 65 holes is called 
a multiple switch base . In an early stage of design, the switch bases 
were separate pieces of masonite; but then it became evident that 
mounting of the hardware to make a machine would be better accom- 
plished by having all the switch bases solidly connected together in 
the panel. 

- 31 - 



5 ^— 



o o o 




o Central 
Pivot Hole 




Arrowhead 
Spoke 2 showing 
positions 
of disc/ 




o o o o o \ Spoke 

Ring: 1 2 3 4 A 




Figure 2-2 — Pattern of the holes in the multiple switch 
(either the "base" in the panel or the "top", 
which is the disc). Also, the system of 
naming the holes. 



The top of a switch is fastened to the base of a switch by means 
of a center pivot , consisting of a long bolt, four hard washers, a 
sponge rubber washer, and a nut; the assembly of the center pivot is 
shown in Figure 2-3. 

The holes (except the center hole) in each switch base and 
switch top are arranged in 4 rings and 16 spokes. The rings are 
called Ring 1, 2, 3, 4 going outward, and the spokes are called 
Spoke 0, 1, 2, 3 and so on around, to Spoke 15. The counting starts 
with the spoke directly to the right, and goes counterclockwise. See 
Figure 2-2. 



- 32 - 



Each of the holes in the switch base may or may not contain a 
. short bolt, called a terminal, for making connections. The connec- 
tions are made using two nuts, one for fastening the bolt securely to 
the switch base, and the second for holding and tightening a wire 
around the bolt so as to make a good electrical connection with the 
bolt (see Figure 2 - 4) . 






Pivot bolt (long bolt), head 



< — Switch top 

^ — Three hard washers 

< — Switch base, or panel 






J 1> 



-Nut 



■ Sponge rubber washer 
- Fourth hard washer 



<-Pivot bolt, shaft 



Figure 2-3 — Center Pivot Assembly 



Terminal bolt (short bolt), 



First small nut 



Connector — > 




Wiper, bent, ridges up 



- Switch base 



^r^?< — Bare wire, looped 
c 2 > tightly around 

kJ ^^^Second nut 



Figure 2-4 — Assembly of Wiper, Terminal Bolt, and 
a Wire Connector 



33 - 



11. Jumpers. Each pair of holes in a switch top, from Ring 1 
to Ring 2 or from Ring 3 to Ring 4 (or very rarely from Ring 2 to ,. 
Ring 3) may or may not contain a jumper, a small piece of brass 
plated metal with two prongs, as shown in Figure 2-5. The two 
prongs fit into holes in the switch disc and are pressed down, like a 
clasp or T fastener, as shown in Figure 2-6. A jumper serves to 
make and break electrical contact as the switch is turned. 



- Jumper prongs 

Jumper body . 

Side view End view 

Figure 2-5 — Jumper, not mounted 




Jumper prongs bent down 




^ Switch top > 

Jumper body > ^^ 

Side view End view 

Figure 2-6 — Jumper, inserted in two adjacent holes along a spoke 



12. Wipers. In between the jumper and the bolt, in the assembled 
multiple switch, is inserted a wiper, a springy piece of phosphor 
bronze with a hole and two small ridges. The shape of the wiper un- 
bent, as it comes in the small envelope, is shown in Figure 2-7. 
The purpose of the wiper is to improve the electrical contact between 
the top of the switch (the disc containing the jumpers) and the bottom 
of the switch (the panel containing the bolts and nuts for the termin- 
als). Patent is being applied for on these wipers. 

The way in which the wiper is assembled is shown in Figure 
2-8, and is as follows: (1) thread the bolt through the wiper, with 
its ridges down; (2) fasten the bolt not too tightly to the panel; 
(3) align the wiper with the spoke (or radius) of the switch; (4) now 
fasten the bolt tightly; (5) bend the wiper gently upwards and over the 



- 34 



bolt, with the ridges up, in such a way that the wiper will slide neatly 
on the jumper, resting in its valley between the ridges; (6) assemble 
the multiple switch with (probably three) washers in between the disc 
and the panel; (7) adjust the amount of bending of the wipers so that 
they push up and down nicely against the jumpers as the switch turns. 

For multiple switches with only two jumpers eveidy spaced, or 
only three jumpers almost evenly spaced, you will not need wipers 
and should not use them , for such switches will work entirely pro- 
perly without wipers. In these cases, you will need to make sure 
that the slots in the heads of the bolts are lined up with the spoke, so 
that the jumpers themselves will position (or detent ) along the spoke 
right above the bolts. (In assembling a switch without wipers, you 
need only one or two spacing washers along the center bolt, not 
three.) For switches with four or more jumpers, you will need 
wipers, for otherwise the switch is likely to work unreliably. 



Hole 



.© 



; Ridges 




t 
Valley 

Wiper, ridges down 

Top view End view 



Figure 2-7 — Unbent wiper 



Ridges of 
wiper 



wiper — ^T ^V< 
bent ^ ir ^ ^-* 



Hr 



- disc 
-jumper 



; wiper bent 
' ^ panel 




Valley 
of wiper 

bolt 



Side view End view 

Figure 2-8 — Assembly of wipers 

- 35 - 



13. Assembly of the Multiple Switches . Before any of the mul- 
tiple switches can function, however, it must first be assembled. 

Into the base we have to insert a number of nuts and bolts to hold 
wire connections and wipers. Just where these are inserted depends 
on the type of switch we desire to construct, two-position, or four- 
position, or some other type. 

Into the top of the switch we must insert a number of jumpers in 
order to make and break contacts. Each jumper is inserted along a 
spoke between one ring and the next. Just where the jumpers are in- 
serted again depends on the type of switch we desire to construct. 

In order for the switch to stay in a position to which it is turned, 
the body of the jumper must line up with the valleys between the 
ridges on the wipers, and these valleys must be in line with the spoke; 
then the jumpers will have a tendency to catch in the valleys, as they 
should, to hold the switch in position (see Figure 2-8, end view). 

Note that in some drawings of the multiple switches, the rings 
and spokes are drawn as thin lines; these lines are not actually 
drawn on the switch discs nor the switch bases; nor do they repres- 
ent electrical lines connecting terminals; instead they are drawn to 
make the arrangement clearer. 

Now suppose we wanted to assemble a switch which would have 
any one of three positions A, B, and C, and which would be capable 
of switching every one of six different circuits. A way in which that 
switch could be assembled is shown in Figure 2 - 9, in which both 
the top and the bottom of the switch are drawn over each other. Six 
jumpers are inserted in the top of the switch, shown as x////a in Fig- 
ure 2-9. It is important that jumpers ordinarily be inserted in 
pairs opposite each other, for reasons of mechanical balancing, so 
that the top of the switch will stay parallel to the bottom of the switch. 
A total of six times six or 36 nuts and bolts are inserted in the bottom 
of the switch, in the spots marked • in Figure 2-9. They are in 
groups of six called decks (also called poles, or levels); these decks 
are electrically independent, and they enable us to switch 6 different 
circuits. In the base, the bolts belonging in any one deck in Ring 1 
or Ring 3 are connected together by wire, as shown by the heavy line; 
they may be connected with one of the short wires 1-1/2 inches long. 
They are made electrically common; in other words, they are com- 
moned. Together they constitute what is called a transfer contact . 



36 - 




Figure 2-9 — Three position switch, six decks (or poles or levels) 



- 37 - 



Let us now consider the layout of the spokes and the rings and the 
64 holes which they produce. We can see that we can assemble a 
switch in a number of different ways. This is the advantage of the 
design of the multiple switch we have chosen (on which patent is being 
applied for). Here are the types of switches that can be made with 
these parts: 

Maximum 
Number of Positions Number of Decks 



2 


16 


3 


10 


4 


8 


5 


6 


6 to 8 


4 


9 to 16 


2 



If nuts and bolts did not cost anything, we could insert 64 nuts 
and bolts into the base of each switch and leave them there — ready 
for use in any switch. Actually, because the kit has a limited supply, 
it may be necessary to move nuts and bolts from one switch to another 
in order to make the different machines we want. 

In the case of jumpers and wipers, we shall fairly often have to 
move them to different places, in order to make different switches 
for different machines. 

14. Additional Material . You may obtain additional or replace- 
ment material for this kit by buying it at a local store, or by writing 

to us. Obviously, if your battery runs down, or if you want more wire, 
or if you want more nuts and bolts, the easy thing to do is to buy them 
in your neighborhood. But for more switch discs or more jumpers, 
etc. , you will probably need to write us. Prices for these items are 
listed on a price list enclosed with the kit or obtainable on request. 

15. Set of Labels . Included in the kit is a set of labels, which 
can be cut out and mounted with cellophane tape or rubber cement on 
the switches, positions, and lights of the various machines so that 
they will be adequately labeled to show what they are doing. 

16. Set of Templates . In work with electrical circuits we need 
to lay out beforehand what we are going to do. We need to design on 
paper how we are to connect the different pieces of material. For 
this purpose, we use circuit diagrams, wiring lists, and templates. 



38 



A Tsircu.it diagram, as mentioned before, shows the scheme of 
connection of batteries, switches, lights, etc., in order to make the 
circuit. In a circuit diagram we pay little attention to the actual phy- 
sical location of the material; we just show a diagram of its arrange- 
ment. 

In a wiring list, we name the. terminals, by words or letters or 
numbers, and we state, for every part of the circuit, what terminal 
is connected to what terminal. In a wiring list again we pay no atten- 
tion to the actual spatial locations of the terminals. For example, if 
without drawing the wire, we write "to. . . ", we are using the principle 
of a wiring list. 

In a template, the case is different; we show the actual wiring 
and the approximate relative spatial location of the different pieces 
of material used in the circuit. In other words, we draw an accurate 
geographical map of where the terminals are, and then we indicate 
the wiring either by drawing lines for the connections or by writing 
notes showing the connections. For the experiments in this manual, 
templates on the actual scale are included in the kit. 

In each experiment in the Tyniac kit, the important part of the 
wiring is on the rear side of the panel. Accordingly, each template 
shows a full scale picture of the rear of the panel. It is therefore a 
mirror image: what is on the right in the drawing in the manual is on 
the left in the template; and vice versa. Of course, some of the in- 
formation appearing on the template belongs on the front side of the 
board: the labels of the switches, their positions, and the lights; and 
the location of the jumpers in the discs. If one pays careful attention 
to the two drawings, one in the manual and one on the template, the 
way the hardware and labels actually are arranged should become quite 
clear. 

17. Trouble -Shooting. After you have wired up a machine, and 
start to play with it, you are likely to find that it does not work entire- 
ly correctly. All engineers worth their salt who do any kind of sig- 
nificant work with electrical circuits discover when they first assemble 
a new piece of equipment that it does not work properly. Finding out 
the reasons why and removing the causes of malfunctioning, the pro- 
cess known as trouble -shooting , therefore is an important and essen- 
tial part of making any piece of equipment start working and stay work - 
ing; and good trouble -shooting is the mark of a good engineer. 



- 39 - 



In order to trouble-shoot, it is helpful to have a systematic and 
logical checklist of questions to be answered one after another, and 
in addition testing apparatus which will tell whether a part of a circuit 
actually does what it is supposed to do. In order to test machines 
made with the Tyniac kit, the essential piece of testing apparatus is 
what is called a continuity tester. A simple form of such a tester is 
a flashlight battery, a lamp, and two wires with bare ends, connected 
as shown in Figure 2-10. Then, when you take the ends of the two 
wires , and touch a certain pair of terminals , if you obtain a light, 
you know that that part of the circuit is connected, is continuous; 
while if you obtain no light, you know that that part of the circuit is 
not connected, is isolated. Then, you compare what your tester 
shows to be actual fact with what you are supposed to have according 
to the circuit diagram, and you have either verified the correctness 
of that part of the circuit, or located some trouble. 

Here are some checklist questions which make a beginning at 
trouble -shooting: 

(1) Does each wire actually make contact with each terminal 

to which it is fastened? 

(2) Does each jumper actually make contact with the wiper 

at each terminal, as its switch turns ? 

(3) Does each lamp really light? 

(4) Is there electricity in the battery? 

(5) Has any wire broken inside its insulation? 

(6) Is there a mistake or typographic error in the diagram 

or the instructions? (This question must always be 
asked, because no author or printer is infallible.) 

(7) Does each wire go where it should? 

(8) Has each label been fastened on in its right place? 

(9) Is each jumper in its right place? 

(10) Is each terminal in its right place? 



*©- 



Figure 2-10 — Continuity Tester 

If you can locate and remove trouble skillfully, you can be well sat- 
isfied with what you have learned. 



40 



Part III: Introduction to Boolean 
Algebra for Circuits and Switching 



In Part I above, we asked the question, "How are circuits like 
those in the experiments designed? "; and we said that one of the best 
approaches to the design of the circuits in the experiments, which 
are examples of what are called switching circuits , is a new kind of 
algebra called Boolean algebra. What is Boolean algebra? 

Briefly, Boolean algebra is the algebra of "AND", "OR", "NOT", 
and conditions, and the technique for manipulating them using sym- 
bols and methods of calculation. Ordinary elementary algebra in- 
cludes the ideas expressed in the words PLUS, TIMES, MINUS, and 
DIVIDED BY, and deals with numbers. In a similar way, Boolean 
algebra includes the ideas expressed in the words AND, OR, NOT, 
and some more very common words and expressions of language 
and logic, and deals with Conditions , classes, and statements. 
Boolean algebra has important applications in the design of any cir- 
cuits that make use of elements that can be either on or off, lighted 
or not lighted, conducting or not conducting — any elements that 
have two mutually exclusive states or conditions. 

Just what are the definitions and rules of Boolean algebra. Why 
is it called "Boolean"? And how does it apply to the design of cir- 
cuits for the experiments in this manual? 

Boolean algebra was named after George Boole, a great Eng- 
lish mathematician who lived 1815-1864. His algebra includes not 
only the ideas expressed by AND, OR NOT, but also the ideas in 
the words: EXCEPT, UNLESS, IF. .. THEN, IF AND ONLY IF, OR 
ELSE, BUT, EITHER. ..OR, NEITHER. .. NOR, BOTH. .. AND, NOT 
BOTH, ALL, NONE, IS (in several of its half dozen meanings), 
LIES IN, IMPLIES, and some more words, excluding however words 
dealing with numerical ideas like MOST, MORE THAN, HALF. 

Boole's great discovery, explained in his book "The Laws of 
Thought", published 1954, was that one actually could make an al- 
gebra out of the words AND, OR, NOT as connectives of classes 
and statements, in a way very similar to ordinary algebra. Boole's 
original form of the algebra did however contain some inconvenient 
and partially incorrect ideas; and his algebra was subsequently 

- 41 - 



greatly improved by other mathematicians, 
Schroder. 



particularly Ernst 



But no one suspected that Boolean algebra could be applied to 
switching circuits until Claude Shannon, who is now a well-known 
mathematician at Bell Telephone Laboratories, pointed out in his 
thesis for the Master's Degree at Massachusetts Institute of Tech- 
nology in 1938, that Boolean algebra could usefully apply to switching 
and relay circuits. This is the application we are interested in here, 
and which we shall now explain. 

Use of Letters . In Boolean algebra applied to switching, the 
same letters are used, a, b, c,. . . . x, y,. ... as are used in ordinary 
algebra. But now they stand not for numbers (which we may or may 
not know), but for the states or conditions of on-off circuit elements, 
(which may be "on" or "off", but we do not know which). For example, 
in Figure 3-1, a stands for the "on-ness" or "off-ness", that is, the 
state , of the on-off switch labeled A, and d stands for the "on-ness" 
or "off-ness" of the light labeled D. (Although the switch has been 
drawn in the off position, because of the location of the jumper, this 
is a regular convention, and does not necessarily mean that the 
Switch A is off. ) 



Source 




Figure 3-1 — A switch and two lights 



- 42 - 



One and Zero. In ordinary algebra the letters a, b, c, . . . stand 
for or represent numbers. For example, a could have the values 7, 
or -3, or 2.67, or -12 1/7 and so forth, for an unlimited collection 
of numbers. If d equals a, then whatever value a has, d has the 
same value. But in Boolean algebra, it is convenient to consider that 
the variables have only the value 1 corresponding with the state ON, 
and the value corresponding with the state OFF. When we say d 
equals a , we mean that whenever a equals 1, d equals 1, and when- 
ever a equals 0, d equals 0. This is of course a much simpler state 
of affairs than in ordinary algebra; and it is surprising how useful 
this simpler algebra of 1 and can still be. 

As we look at Figure 3-1, we can see that Light D is on if and 
only if Switch A is on, and Light C is on if and only if Switch A is off. 
We express this by saying that the state of D equals the state of A, 
that is to say, that d equals a. 

The Operator NOT. Let us look now at the Light C in Figure 
3-1. It is on if and only if the switch is off, and it is off if and only 
if the switch is on. We can summarize this state of affairs in the 
following table: 



a 


c 





1 


1 






In Boolean algebra, we say that the slate c equals the negative of the 
state a, and we write c=s NOT-a= a'', which is read a prime or 
not— a. If we should look for a formula of ordinary algebra which 
would give the same result, we could say that c = l — a; other form- 
ulas could be used but this is the simplest. 

The Operator OR. a OR b is represented by the circuit shown 
in Figure 3 - 2, a parallel circuit. 




Switch A 



Switch B 



Light C 



c = a OR b = a v b 



Figure 3-2 
- 43 - 



Looking at Figure 3-2, we can see that the way in which the circuit 
is wired provides that Light C will be on if Switch A is on or if Switch 
B is on or if both are on. In other words the state c of the light is * 
equal to a or b, where the following table defines OR for every 
possible case: 



a 


b 


c 














1 


1 


1 





1 


1 


1 


1 



In Boolean algebra, we write c = a v b, which is read a vee b or . 
a or b. If we should look for a formula of ordinary algebra which 
would give the same result, we could say that c = a-f-b— ab, a plus 
b minus the product of a and b; other formulas could be used but 
this one is the simplest. 

The Operator AND, a AND b is represented by the circuit 
shown in Figure 3 - 3, a series circuit. 



Source 




Light C 



Switch A 



Switch B 



c — a AND b = a»b = ab 



Figure 3-3 



Looking at Figure 3-3, we can see that the way in which the circuit 
is wired provides that Light C will be on if and only if Switch A is 
on and Switch B is on. In other words the state c of the light is 
equal to a AND b both, where the following table completely defines 
AND: 



a 


b 


c 














1 





1 








1 


1 


1 



- 44 



In Boolean algebra, we write c= a»b or c = ab, which is read a TIMES 
b or a AND b or a dot b or ab. This is the same operation as multi- 
plication in ordinary algebra. 

Other Connectives and Operators. We can now define EXCEPT, 
a EXCEPT b is the same as a AND NOT b: a»b\ Also, we can now 
define a OR ELSE b; this is the same as a AND NOT h OR b AND NOT 
a: a'b'vb'a'. And we can define many more of the common words 
of language. 

Every now and then we find a case of ambiguity. OR for example 
is ambiguous. Sometimes it means AND/OR. This is the OR which 
is the OR of Boolean algebra defined above, and of two switches in 
parallel. Sometimes OR means OR ELSE. This is the OR we have 
just defined above as OR ELSE. 

A rather full discussion of problems of translating ordinary 
English into Boolean algebra is contained in two short publications 
of ours, P 5: "Boolean Algebra and Applications to Insurance' 1 and 
P4: " A Summary of Symbolic Logic and its Practical Applications" 
(both are available from us). 

Rules of Boolean Algebra . Some of the more important rules of 
Boolean algebra are given below with their translations: 

avb=bva a OR b is the same as b OR a 

(avb)vc a av(bvc) (a OR b) OR c is the same as a OR 

(bOR c) 
a(bvc)=abvac a AND (b OR c) equals (a AND b) 

OR (a AND cj 
a v be = (a v b) (a v c) a OR (b AND c) equals (a OR b) 

AND (a OR c) 
a v a= a a OR a is the same as a 

aa= a a AND a is the same as a 

avO=a a OR off-ness (zero) is the same 

as a 
a* 1= a a AND on-ness (one) is the same 

as a 
a v 1= 1 a OR on-ness (one) is the same as 

on-ness (one) 
a» 0= a AND off-ness (zero) is the same 

as off-ness (zero) 
a v a'=l a OR NOT-a equals on-ness (one) 

a-a'= a AND NOT-a equals off-ness (zero) 

- 45 - 



(a v b)'=a'. b' 


NOT- (a OR b) equals NOT-a AND 




NOT-b 


(ab)'=a' v b' 


NOT (BOTH a AND fc) equals 




NOT-a OR NOT-b 


ab v ab T = a 


(a AND b) OR (a AND NOT-b) 




equals a 


(a v b) (a vb')=a 


(a OR b) AND (a OR NOT-b) 




equals a 


(a ! )'= a 


NOT-NOT-a is the same as a 


PaO 


NOT-on equals off 


O f = l 


NOT-off equals on 



Considerably fuller summaries of Boolean algebra appear in our 
two publications P5 and P4 mentioned above. 

A Sample Problem . Let us now consider a sample problem. 
Suppose we try to design part of the circuit for Experiment 6, The 
Two Suspicious Husbands at Great North Bay. Suppose we try to 
turn into a circuit: "They agree that the wife of either one may not 
go boating alone with the other husband". Then there are two cases 
for which the danger light should shine, reported in the following 
table, where S means yes, and X means no. 







In the Boat: 






George 


Harry Violet 


Winifred 


(1) 


iS 


X X 


i/ 


(2,) 


X 


iS iS 


X 



Let G, H, V, W stand for the states of switches that when they 
are in their "on" position mean that George, Harry, Violet, Wini- 
fred, respectively, are "in the boat". Then, in the Boolean algebra 
of switching circuits, these cases will be expressed as: G-H'-V* 
W v G'» H»V # W f . In a completely diagrammed circuit therefore 
they appear as shown in Figure 3-4. In each line in the circuit, we 
have shown the "information" or Boolean expression which it contains, 
as a result of the switches between it and the source of current. 

Conclusion . This then is a very brief introduction to Boolean 
algebra and its application to switching circuits. It is a useful and 
powerful tool, though not the only one, in the design of switching 
circuits. And people will doubtless find out and learn more and more 
interesting and important applications of Boolean algebra as people 
become more and more accustomed to regarding AND, OR, and NOT 



- 46 



as operators for calculating with, much like the operators PLUS, 
MINUS,* TIMES, and DIVIDED BY, yet of course far more frequent 
in the affairs of men. 

For more information about Boolean algebra and its applications, 
we again refer readers to our publications P5 and P4. 



N\ In 
~^}fij| Not in 



George 



'G"H' 



Harry 



ID anger 



G'-H-V- 



Violet 



In / 


\ln/ V GH'V'W 
Jr \4- v 


(Not in/ r™\ 


^L t A'0-H.V.W' 


^^ Vg-h'-v^/ 


/ OH-VW 


Winifred 




Figure 3-4 





47